Mohammed Ali
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Mohammed Ali has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
- Hussain Al-Qassem
Department of Mathematics and Statistics, Qatar University, Doha 2713, Qatar
19 shared publications - Oqlah Al-Refai
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13132, Jordan
6 shared publications - Imad Jaradat
Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
5 shared publications - Marwan Alquran
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
3 shared publications - Ahmad Al Azab
Department of Basic Science, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Ibra 400, Oman
2 shared publications - Amer Darweesh
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
2 shared publications
Latest Publications
- Open Access
New Results on Certain Subclasses of Univalent Functions Defined by the nth Derivative of z/f(z)
For , we study the subclass of univalent functions f with in which the whole allowance of the Al-Refai–Darus criterion is assigned to the nth derivative of . The map is a bijection of onto a closed ball of , which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the -fold symmetric extremal functions ; the exact region of , whose boundary is attained by Möbius parameters written in closed form; an exact radius for dilations of products , sharp both for Aksentev’s inequality and for univalence. The vanishing of does not by itself imply n-fold symmetry; the n-fold symmetric members of correspond exactly to with g in the same ball, which provides the exact region of . For the larger class defined by and the criterion, we obtain sharp bounds as well. The comparison with n-fold symmetric univalent functions records a gap; it is not a sharpening of known results.Open AccessNew Results on Certain Subclasses of Univalent Functions Defined by the nth Derivative of z/f(z)
For , we study the subclass of univalent functions f with in which the whole allowance of the Al-Refai–Darus criterion is assigned to the nth derivative of . The map is a bijection of onto a closed ball of , which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the -fold symmetric extremal functions ; the exact region of , whose boundary is attained by Möbius parameters written in closed form; an exact radius for dilations of products , sharp both for Aksentev’s inequality and for univalence. The vanishing of does not by itself imply n-fold symmetry; the n-fold symmetric members of correspond exactly to with g in the same ball, which provides the exact region of . For the larger class defined by and the criterion, we obtain sharp bounds as well. The comparison with n-fold symmetric univalent functions records a gap; it is not a sharpening of known results. - Open Access
- 14 October 2026
- Published by MDPI AG in Preprints.org
Sharp Estimates and Symmetric Subclasses for Univalent Functions Defined by the nth Derivative of z/f(z)
The Al-Refai--Darus criterion guarantees univalence of a normalized function \( f \) when a weighted sum of \( |(z/f)^{(k)}(0)| \), \( 2\le k\le n-1 \), and of \( \sup|(z/f)^{(n)}| \) does not exceed \( 1 \). For \( n\ge3 \) we study the subclass \( \mathcal C_n \) with \( a_2=\dots=a_n=0 \), in which the whole allowance goes to the \( n \) th derivative. The map \( f\mapsto(z/f)^{(n)} \) is a bijection of \( \mathcal C_n \) onto a closed ball of \( H^\infty \), which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the \( (n+j) \)-fold symmetric extremal functions \( z/(1+cz^{n+j}) \); the exact region of \( (a_{n+1},a_{n+2}) \), whose boundary is attained by M\"obius parameters written in closed form; and an exact radius for dilations of products \( f_1f_2/z \), sharp both for Aksentev's inequality and for univalence. The \( n \)-fold symmetric members of \( \mathcal C_n \) correspond to \( g(z^n) \) with \( g \) in the same ball, which gives the exact region of \( (a_{n+1},a_{2n+1}) \). For the larger class defined by \( a_2=0 \) and the criterion we obtain sharp bounds as well. The comparison with \( n \)-fold symmetric univalent functions records a gap; it is not a sharpening of known results.- 14 October 2026
- Published by MDPI AG in Preprints.org
Open AccessSharp Estimates and Symmetric Subclasses for Univalent Functions Defined by the nth Derivative of z/f(z)
The Al-Refai--Darus criterion guarantees univalence of a normalized function \( f \) when a weighted sum of \( |(z/f)^{(k)}(0)| \), \( 2\le k\le n-1 \), and of \( \sup|(z/f)^{(n)}| \) does not exceed \( 1 \). For \( n\ge3 \) we study the subclass \( \mathcal C_n \) with \( a_2=\dots=a_n=0 \), in which the whole allowance goes to the \( n \) th derivative. The map \( f\mapsto(z/f)^{(n)} \) is a bijection of \( \mathcal C_n \) onto a closed ball of \( H^\infty \), which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the \( (n+j) \)-fold symmetric extremal functions \( z/(1+cz^{n+j}) \); the exact region of \( (a_{n+1},a_{n+2}) \), whose boundary is attained by M\"obius parameters written in closed form; and an exact radius for dilations of products \( f_1f_2/z \), sharp both for Aksentev's inequality and for univalence. The \( n \)-fold symmetric members of \( \mathcal C_n \) correspond to \( g(z^n) \) with \( g \) in the same ball, which gives the exact region of \( (a_{n+1},a_{2n+1}) \). For the larger class defined by \( a_2=0 \) and the criterion we obtain sharp bounds as well. The comparison with \( n \)-fold symmetric univalent functions records a gap; it is not a sharpening of known results. - Open Access
- 17 August 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (8) , 566
Fekete–Szegő and Second Hankel Determinant Problems for a Bounded-Second-Derivative Class of Univalent Functions, and Its Fractional-Derivative Extension
Let denote the class of functions analytic and normalized in , and let . We give a short, self-contained proof that D consists entirely of univalent functions by a direct line-integral estimate combined with the classical Noshiro–Warschawski theorem. We then solve, in closed form and with explicit extremal functions, two classical extremal coefficient problems for D: the Fekete–Szegő problem and the second Hankel determinant, using the exact Schur parametrization of bounded analytic functions applied to . We also establish a sharp bound on a single coefficient for every , obtained by an elementary Parseval argument that does not require the full joint Schur parametrization needed for the Fekete–Szegő and Hankel problems. We then compose D with the Owa–Srivastava fractional derivative operator (), used to build fractional bi-univalent subclasses, to define the one-parameter family , and extend all three results to , again with explicit extremal functions. Because the underlying weights grow at different rates in the fractional parameter , the Fekete–Szegő problem exhibits a genuine, monotone bifurcation as ranges over , while the Hankel and general-coefficient bounds decrease monotonically—effects that are structural consequences of the fractional operator rather than a simple rescaling of the classical case. All results are verified in two independent numerical ways: the Schur parametrization lemma itself is checked against an explicit, independently constructed rational Schur function whose Taylor coefficients are extracted numerically via the Cauchy integral formula, and the sharp bounds are checked by Monte Carlo maximization over the admissible Schur parameters. Both checks are explained in detail and agree with the closed forms to at least four decimal places. Unlike the Carathéodory class of functions with positive real part, whose coefficient body is fixed at the origin (value 1) and is classically parametrized without an extra recursive step, the Schur class used here does not pin down , so its exact coefficient body genuinely requires the two-step recursive Schur parametrization applied below to ; identifying and exploiting this distinction is part of the technical contribution of the paper.- 17 August 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (8) , 566
Open AccessFekete–Szegő and Second Hankel Determinant Problems for a Bounded-Second-Derivative Class of Univalent Functions, and Its Fractional-Derivative Extension
Let denote the class of functions analytic and normalized in , and let . We give a short, self-contained proof that D consists entirely of univalent functions by a direct line-integral estimate combined with the classical Noshiro–Warschawski theorem. We then solve, in closed form and with explicit extremal functions, two classical extremal coefficient problems for D: the Fekete–Szegő problem and the second Hankel determinant, using the exact Schur parametrization of bounded analytic functions applied to . We also establish a sharp bound on a single coefficient for every , obtained by an elementary Parseval argument that does not require the full joint Schur parametrization needed for the Fekete–Szegő and Hankel problems. We then compose D with the Owa–Srivastava fractional derivative operator (), used to build fractional bi-univalent subclasses, to define the one-parameter family , and extend all three results to , again with explicit extremal functions. Because the underlying weights grow at different rates in the fractional parameter , the Fekete–Szegő problem exhibits a genuine, monotone bifurcation as ranges over , while the Hankel and general-coefficient bounds decrease monotonically—effects that are structural consequences of the fractional operator rather than a simple rescaling of the classical case. All results are verified in two independent numerical ways: the Schur parametrization lemma itself is checked against an explicit, independently constructed rational Schur function whose Taylor coefficients are extracted numerically via the Cauchy integral formula, and the sharp bounds are checked by Monte Carlo maximization over the admissible Schur parameters. Both checks are explained in detail and agree with the closed forms to at least four decimal places. Unlike the Carathéodory class of functions with positive real part, whose coefficient body is fixed at the origin (value 1) and is classically parametrized without an extra recursive step, the Schur class used here does not pin down , so its exact coefficient body genuinely requires the two-step recursive Schur parametrization applied below to ; identifying and exploiting this distinction is part of the technical contribution of the paper. - Open Access
- 11 June 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (12) , 2099
Generalized Marcinkiewicz Integral Operators Along Certain Surfaces
In this article, a class of rough generalized Marcinkiewicz operators is considered. Under the condition that the singular kernel belongs to the space , the boundedness of these operators is confirmed from the space of homogeneous Triebel–Lizorkin functions to the space. Moreover, appropriate bounds are obtained which allow us to utilize Yano’s extrapolation procedure to prove the boundedness of the aforementioned operators under weaker assumptions on the kernels. In this work, several known past results are generalized, extended, and improved.- 11 June 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (12) , 2099
Open AccessGeneralized Marcinkiewicz Integral Operators Along Certain Surfaces
In this article, a class of rough generalized Marcinkiewicz operators is considered. Under the condition that the singular kernel belongs to the space , the boundedness of these operators is confirmed from the space of homogeneous Triebel–Lizorkin functions to the space. Moreover, appropriate bounds are obtained which allow us to utilize Yano’s extrapolation procedure to prove the boundedness of the aforementioned operators under weaker assumptions on the kernels. In this work, several known past results are generalized, extended, and improved. - Open Access
- 8 May 2026
- Published by MDPI AG in Preprints.org
Generalized Marcinkiewicz Integral Operators Along Certain Surfaces
In this article, a class of rough generalized Marcinkiewicz operators is considered. Under the condition that the singular kernel belongs to the space Lq(Bs−1), the boundedness of these operators are confirmed from the space of homogeneous Triebel–Lizorkin functions to the Lp(Rd+1) space. Moreover, appropriate Lp bounds are obtained which allow us to utilize Yano’s extrapolation procedure to prove the boundedness of the aforementioned operators under weaker assumptions on the kernels. In this work, several known past results are generalized, extended, and improved.
- 8 May 2026
- Published by MDPI AG in Preprints.org
Open AccessGeneralized Marcinkiewicz Integral Operators Along Certain Surfaces
In this article, a class of rough generalized Marcinkiewicz operators is considered. Under the condition that the singular kernel belongs to the space Lq(Bs−1), the boundedness of these operators are confirmed from the space of homogeneous Triebel–Lizorkin functions to the Lp(Rd+1) space. Moreover, appropriate Lp bounds are obtained which allow us to utilize Yano’s extrapolation procedure to prove the boundedness of the aforementioned operators under weaker assumptions on the kernels. In this work, several known past results are generalized, extended, and improved.
- Open Access
- 9 April 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (8) , 1244
Boundedness of Rough Multiple Oscillatory Singular Integral Operators on Triebel–Lizorkin Space
In this article, we investigate oscillatory singular integral operators on product domains. We establish the boundedness of these operators on Triebel–Lizorkin spaces under weak assumptions on the rough kernel functions. Our results extend several known results from the one-parameter setting to the two-parameter setting.
- 9 April 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (8) , 1244
Open AccessBoundedness of Rough Multiple Oscillatory Singular Integral Operators on Triebel–Lizorkin Space
In this article, we investigate oscillatory singular integral operators on product domains. We establish the boundedness of these operators on Triebel–Lizorkin spaces under weak assumptions on the rough kernel functions. Our results extend several known results from the one-parameter setting to the two-parameter setting.
- Open Access
Weighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions
In this paper we investigate the weighted boundedness of generalized Marcinkiewicz integrals over multiple symmetric domains. Under the conditions , , we establish suitable weighted bounds for the integrals . These bounds are combined with Yano’s extrapolation argument to obtain the weighted boundedness of from the Triebel–Lizorkin space to the space under the weaker conditions . Our findings are essential improvements and extension of several known findings in the literature.Open AccessWeighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions
In this paper we investigate the weighted boundedness of generalized Marcinkiewicz integrals over multiple symmetric domains. Under the conditions , , we establish suitable weighted bounds for the integrals . These bounds are combined with Yano’s extrapolation argument to obtain the weighted boundedness of from the Triebel–Lizorkin space to the space under the weaker conditions . Our findings are essential improvements and extension of several known findings in the literature. - Open Access
- 24 December 2025
- Published by MDPI AG in Preprints.org
Weighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions
In this paper we investigate the weighted $L^p$ boundedness of generalized Marcinkiewicz integrals $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$ over multiple symmetric domains. Under the conditions $\mathbf{K}\in L^{q}( \mathbb{B}^{{{m}}-1}\times \mathbb{B}% ^{{{n}}-1})$, $q>1$, we stablish suitable weighted $L^p$ bounds for the integrals $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$. These bounds are combined with an extrapolation argument of Yano so we obtain the weighted $L^p$ boundedness of $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$ from the Triebel-Lizorkin space $\overset{.}{F}_{p}^{0,\varepsilon}(\omega_1,\omega_2)$ to the space $L^p(\omega_1,\omega_2)$ under the weak conditions $\mathbf{K}$ lie in the space $ B_q^{(0,\frac{2}{\varepsilon}-1)}(\mathbb{B}^{m-1}\times\mathbb{B}% ^{n-1})$ or in the space $L(\log L)^{2/\varepsilon}(\mathbb{B}^{m-1}\times\mathbb{B}% ^{n-1})$. Our findings are essential improvements and extension of several known findings in the literature.- 24 December 2025
- Published by MDPI AG in Preprints.org
Open AccessWeighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions
In this paper we investigate the weighted $L^p$ boundedness of generalized Marcinkiewicz integrals $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$ over multiple symmetric domains. Under the conditions $\mathbf{K}\in L^{q}( \mathbb{B}^{{{m}}-1}\times \mathbb{B}% ^{{{n}}-1})$, $q>1$, we stablish suitable weighted $L^p$ bounds for the integrals $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$. These bounds are combined with an extrapolation argument of Yano so we obtain the weighted $L^p$ boundedness of $\mathcal{M}^{(\varepsilon)}_{\mathbf{K}}$ from the Triebel-Lizorkin space $\overset{.}{F}_{p}^{0,\varepsilon}(\omega_1,\omega_2)$ to the space $L^p(\omega_1,\omega_2)$ under the weak conditions $\mathbf{K}$ lie in the space $ B_q^{(0,\frac{2}{\varepsilon}-1)}(\mathbb{B}^{m-1}\times\mathbb{B}% ^{n-1})$ or in the space $L(\log L)^{2/\varepsilon}(\mathbb{B}^{m-1}\times\mathbb{B}% ^{n-1})$. Our findings are essential improvements and extension of several known findings in the literature. - Open Access
- 14 April 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (8) , 1287
On Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces
In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by }. We establish the -boundedness of these integrals when the kernel functions lie in the space. Combining this result with Yano’s extrapolation technique, we further obtain the -boundedness under weaker kernel conditions—specifically, when the kernels belong to either the block space or . Our results extend and refine several previously known results on Marcinkiewicz integrals, offering broader applicability and sharper conclusions.- 14 April 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (8) , 1287
Open AccessOn Rough Parametric Marcinkiewicz Integrals Along Certain Surfaces
In this paper, we study rough Marcinkiewicz integrals associated with surfaces defined by }. We establish the -boundedness of these integrals when the kernel functions lie in the space. Combining this result with Yano’s extrapolation technique, we further obtain the -boundedness under weaker kernel conditions—specifically, when the kernels belong to either the block space or . Our results extend and refine several previously known results on Marcinkiewicz integrals, offering broader applicability and sharper conclusions. - Open Access
- 12 April 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (8) , 1273
Advances in Clinical Trial Design: Employing Adaptive Multiple Testing and Neyman Allocation for Unequal Samples
This study introduces a new method that combines three distinct approaches for comparing two treatments: Neyman allocation, the O’Brien and Fleming multiple testing procedure, and a system of different sample weights at different stages. This new approach is called the Neyman Weighted Multiple Testing Procedure (NWMP). Each of these adaptive designs “individually” has proven beneficial for clinical research by removing constraints that can limit clinical trials. The advantages of these three methods are merged into a single, innovative approach that demonstrates increased efficiency in this work. The multiple testing procedure allows for trials to be stopped before their chosen time frame if one treatment is more effective. Neyman allocation is a statistically sound method designed to enhance the efficiency and precision of estimates. It strategically allocates resources or sample sizes to maximize the quality of statistical inference, considering practical constraints. Additionally, using different weights in this method provides greater flexibility, allowing for the effective distribution of sample sizes across various stages of the research. This study demonstrates that the new method maintains similar efficiency in terms of the Type I error rate and statistical power compared to the O’Brien and Fleming test while offering additional flexibility. Furthermore, the research includes examples of both real and hypothetical cases to illustrate the developed procedure.
- 12 April 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (8) , 1273
Open AccessAdvances in Clinical Trial Design: Employing Adaptive Multiple Testing and Neyman Allocation for Unequal Samples
This study introduces a new method that combines three distinct approaches for comparing two treatments: Neyman allocation, the O’Brien and Fleming multiple testing procedure, and a system of different sample weights at different stages. This new approach is called the Neyman Weighted Multiple Testing Procedure (NWMP). Each of these adaptive designs “individually” has proven beneficial for clinical research by removing constraints that can limit clinical trials. The advantages of these three methods are merged into a single, innovative approach that demonstrates increased efficiency in this work. The multiple testing procedure allows for trials to be stopped before their chosen time frame if one treatment is more effective. Neyman allocation is a statistically sound method designed to enhance the efficiency and precision of estimates. It strategically allocates resources or sample sizes to maximize the quality of statistical inference, considering practical constraints. Additionally, using different weights in this method provides greater flexibility, allowing for the effective distribution of sample sizes across various stages of the research. This study demonstrates that the new method maintains similar efficiency in terms of the Type I error rate and statistical power compared to the O’Brien and Fleming test while offering additional flexibility. Furthermore, the research includes examples of both real and hypothetical cases to illustrate the developed procedure.