Irshad Ayoob
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Irshad Ayoob has a total of 16 co-authors. Here are the top co-authors by number of shared publications:
- Nabil Mlaiki
Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
5 shared publications - Zhen Chuan Ng
Universiti Sains Malaysia
2 shared publications - Abdelbasset Felhi
Department of Mathematics and Physics, Preparatory Engineering Institute, Bizerte, Carthage University, Tunisia
1 shared publication Adeeba Rafi
University of Sargodha, Pakistan
1 shared publication- Amna Naz
Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan
1 shared publication - Dur-E-Shehwar Sagheer
Department of Mathematics Capital University of Science and Technology Islamabad Pakistan
1 shared publication
Latest Publications
- Open Access
- 5 September 2026
- Published by Elsevier in Results in Applied Mathematics
- Vol. 31
Applications of double composed metric space to integral and functional equations
- 5 September 2026
- Published by Elsevier in Results in Applied Mathematics
- Vol. 31
Open AccessApplications of double composed metric space to integral and functional equations
- Open Access
- 1 January 2026
- Published by Wiley in International Journal of Mathematics and Mathematical Sciences
- Vol. 2026 (1)
A Generalization of Ramanujan‐Type Integrals
Recently, Xu, Yin, and Zhou obtained explicit evaluations of the Ramanujan‐type integrals and expressing them in closed form in terms of the gamma function, the Riemann zeta function, and the alternating zeta function. In the present paper, we generalize these formulas from the special Mellin kernel x s −1 to a general real‐valued measurable function f and evaluate the two integral transforms and where a > 0, , and f satisfies suitable Laplace‐transform and summability assumptions. If denotes the Laplace transform of f , then we prove the exact representations and Thus, our results may be viewed as functional extensions of Xu’s formulas. As applications, we recover the known Mellin‐type evaluations by taking f ( x ) = x s −1 , and we derive further explicit corollaries for f ( x ) = x s −1 e − c x and f ( x ) = x e − c x , leading respectively to identities involving special functions.
- 1 January 2026
- Published by Wiley in International Journal of Mathematics and Mathematical Sciences
- Vol. 2026 (1)
Open AccessA Generalization of Ramanujan‐Type Integrals
Recently, Xu, Yin, and Zhou obtained explicit evaluations of the Ramanujan‐type integrals and expressing them in closed form in terms of the gamma function, the Riemann zeta function, and the alternating zeta function. In the present paper, we generalize these formulas from the special Mellin kernel x s −1 to a general real‐valued measurable function f and evaluate the two integral transforms and where a > 0, , and f satisfies suitable Laplace‐transform and summability assumptions. If denotes the Laplace transform of f , then we prove the exact representations and Thus, our results may be viewed as functional extensions of Xu’s formulas. As applications, we recover the known Mellin‐type evaluations by taking f ( x ) = x s −1 , and we derive further explicit corollaries for f ( x ) = x s −1 e − c x and f ( x ) = x e − c x , leading respectively to identities involving special functions.
- Open Access
- 22 December 2025
- Published by Springer Nature in Fixed Point Theory and Algorithms for Sciences and Engineering
- Vol. 2025 (1)
Banach fixed point theorem for fractional integral contraction
- 22 December 2025
- Published by Springer Nature in Fixed Point Theory and Algorithms for Sciences and Engineering
- Vol. 2025 (1)
Open AccessBanach fixed point theorem for fractional integral contraction
- Open Access
- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 7023
Generalization of an Integral Related to Stieltjes Moment Problem
In connection with the non-uniqueness of the Stieltjes moment problem on $(0,\infty)$, Stieltjes constructed the nontrivial function $ f(x)=e^{-x^{1/4}}\sin\!\big(x^{1/4}\big) $ satisfying $\int_{0}^{\infty} x^{n}f(x)\,dx=0$ for all integers $n\ge 0$. We extend this by considering \[ I(k)=\int_{0}^{\infty} e^{-x^{1/4}}\sin\!\big(x^{1/4}\big)\,x^{k}\,dx \] for real $k\ge 0$, evaluating $I(k)$ explicitly and proving $I(k)=0$ if and only if $k\in\mathbb{Z}_{\ge 0}$. More generally, for parameters $m>0$, $\alpha>0$, $\beta\in\mathbb{R}$, $q,k\in\mathbb{R}$ we analyze \[ I_{m,q}(k;\alpha,\beta)=\int_{0}^{\infty} e^{-\alpha x^{1/m}}\sin\!\big(\beta x^{1/m}\big)\,x^{k}(x^{1/m})^{q}\,dx, \] derive a closed form, and give necessary and sufficient conditions for its vanishing. We also establishcosine analogues, both for the Stieltjes example and for the generalized integral mentioned above.As a consequence, we obtain integral representations of Γ(A) for suitable A > 0, as well as integralformulas for several classical constants arising from gamma function. To understand the importanceof integrals that vanish for every value of a continuous parameter, we will also discuss Salem’sequivalence of the Riemann hypothesis, which is formulated in terms of such a parameter-dependentintegral.- 5 November 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (4) , 7023
Open AccessGeneralization of an Integral Related to Stieltjes Moment Problem
In connection with the non-uniqueness of the Stieltjes moment problem on $(0,\infty)$, Stieltjes constructed the nontrivial function $ f(x)=e^{-x^{1/4}}\sin\!\big(x^{1/4}\big) $ satisfying $\int_{0}^{\infty} x^{n}f(x)\,dx=0$ for all integers $n\ge 0$. We extend this by considering \[ I(k)=\int_{0}^{\infty} e^{-x^{1/4}}\sin\!\big(x^{1/4}\big)\,x^{k}\,dx \] for real $k\ge 0$, evaluating $I(k)$ explicitly and proving $I(k)=0$ if and only if $k\in\mathbb{Z}_{\ge 0}$. More generally, for parameters $m>0$, $\alpha>0$, $\beta\in\mathbb{R}$, $q,k\in\mathbb{R}$ we analyze \[ I_{m,q}(k;\alpha,\beta)=\int_{0}^{\infty} e^{-\alpha x^{1/m}}\sin\!\big(\beta x^{1/m}\big)\,x^{k}(x^{1/m})^{q}\,dx, \] derive a closed form, and give necessary and sufficient conditions for its vanishing. We also establishcosine analogues, both for the Stieltjes example and for the generalized integral mentioned above.As a consequence, we obtain integral representations of Γ(A) for suitable A > 0, as well as integralformulas for several classical constants arising from gamma function. To understand the importanceof integrals that vanish for every value of a continuous parameter, we will also discuss Salem’sequivalence of the Riemann hypothesis, which is formulated in terms of such a parameter-dependentintegral. - Open Access
- 5 October 2025
- Published by Elsevier in Case Studies in Thermal Engineering
- Vol. 75
Convective stability in porous structures for energy and biosensing applications using viscosity-driven flow control and couple-stress fluid
- 5 October 2025
- Published by Elsevier in Case Studies in Thermal Engineering
- Vol. 75
Open AccessConvective stability in porous structures for energy and biosensing applications using viscosity-driven flow control and couple-stress fluid
- Open Access
- 1 August 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (3) , 6575
On the Evaluation of Certain Unsolved Definite Integrals
We study the following three definite integrals, previously posed as open problems by another researcher: \( I(\alpha) = \int_0^{\infty} x^{-1/2} \ln(1 + x^{-\alpha})\,dx \), \( I_n(\alpha) = \int_0^{\infty} \frac{1}{\sqrt{x}(x^2 + 4\alpha^2)^n}\,dx \), and \( I(\beta)=\int_0^{\infty} x^{-3/2} \big[f(2\beta/x) - f(2/x)\big]\,dx \). We establish sufficient conditions for the convergence of these integrals and evaluate them in closed form using special functions. In particular, the third integral $I(\beta)$ turns out to be similar to Frullani integral, and we obtain two interesting formulas for this integral. These types ofintegrals have been used to establish logarithmic Hardy-Hilbert-type inequalities.- 1 August 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (3) , 6575
Open AccessOn the Evaluation of Certain Unsolved Definite Integrals
We study the following three definite integrals, previously posed as open problems by another researcher: \( I(\alpha) = \int_0^{\infty} x^{-1/2} \ln(1 + x^{-\alpha})\,dx \), \( I_n(\alpha) = \int_0^{\infty} \frac{1}{\sqrt{x}(x^2 + 4\alpha^2)^n}\,dx \), and \( I(\beta)=\int_0^{\infty} x^{-3/2} \big[f(2\beta/x) - f(2/x)\big]\,dx \). We establish sufficient conditions for the convergence of these integrals and evaluate them in closed form using special functions. In particular, the third integral $I(\beta)$ turns out to be similar to Frullani integral, and we obtain two interesting formulas for this integral. These types ofintegrals have been used to establish logarithmic Hardy-Hilbert-type inequalities. - Open Access
- 1 May 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (2) , 6089
Generalized Fractional Integral Extensions of Hermite-Hadamard Inequalities via Extended Mittag-Leffler Kernel
In this article, we provid a number of Hermite-Hadamard type fractional integral inequalities for the Atangana-Baleanu and Prabhakar fractional operators, using extended generalized Mittag-Leffler functions as their kernel. Significant findings are provided for the integral inequalities involving fractional integrals of the type $({{\Im_1}}+, {{\Im_2}}-)$ and $(\frac{{{\Im_1}} + {{\Im_2}}}{2})$. By employing certain functions to create visual graphs with matching numerical entries that depict the inequalities, we show the veracity of our findings.- 1 May 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (2) , 6089
Open AccessGeneralized Fractional Integral Extensions of Hermite-Hadamard Inequalities via Extended Mittag-Leffler Kernel
In this article, we provid a number of Hermite-Hadamard type fractional integral inequalities for the Atangana-Baleanu and Prabhakar fractional operators, using extended generalized Mittag-Leffler functions as their kernel. Significant findings are provided for the integral inequalities involving fractional integrals of the type $({{\Im_1}}+, {{\Im_2}}-)$ and $(\frac{{{\Im_1}} + {{\Im_2}}}{2})$. By employing certain functions to create visual graphs with matching numerical entries that depict the inequalities, we show the veracity of our findings. - Open Access
- 1 May 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (2) , 6015
On Multivalued Contractions via θ-hyperbolic Sine Distance Functions
Very recently, the concept of θ-hyperbolic sine distance functions has been introduced by Jleli and Samet in [14]. In this work, we prove some related fixed points results for several classes of multivalued mappings including manageable functions on metric spaces.
- 1 May 2025
- Published by New York Business Global LLC in European Journal of Pure and Applied Mathematics
- Vol. 18 (2) , 6015
Open AccessOn Multivalued Contractions via θ-hyperbolic Sine Distance Functions
Very recently, the concept of θ-hyperbolic sine distance functions has been introduced by Jleli and Samet in [14]. In this work, we prove some related fixed points results for several classes of multivalued mappings including manageable functions on metric spaces.
- Open Access-Contractions Endowed with Mann’s Iterative Scheme in Convex -Metric SpacesRecently, Ji et al. established certain fixed-point results using Mann’s iterative scheme tailored to -metric spaces. Stimulated by the notion of the -contraction introduced by Wardoski, the contraction condition of Ji et al. was generalized in this research. Several fixed-point results with Mann’s iterative scheme endowed with -contractions in -metric spaces were proven. One non-trivial example was elaborated to support the main theorem. Moreover, for application purposes, the existence of the solution to an integral equation is provided by using the axioms of the proven result. The obtained results are generalizations of several existing results in the literature. Furthermore, the results of Ji. et al. are the special case of theorems provided in the present research.Open Access-Contractions Endowed with Mann’s Iterative Scheme in Convex -Metric SpacesRecently, Ji et al. established certain fixed-point results using Mann’s iterative scheme tailored to -metric spaces. Stimulated by the notion of the -contraction introduced by Wardoski, the contraction condition of Ji et al. was generalized in this research. Several fixed-point results with Mann’s iterative scheme endowed with -contractions in -metric spaces were proven. One non-trivial example was elaborated to support the main theorem. Moreover, for application purposes, the existence of the solution to an integral equation is provided by using the axioms of the proven result. The obtained results are generalizations of several existing results in the literature. Furthermore, the results of Ji. et al. are the special case of theorems provided in the present research.
- Open Access
- 14 April 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (8) , 1866
Double-Composed Metric Spaces
The double-controlled metric-type space is a metric space in which the triangle inequality has the form for all . The maps are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form for all . In our new space, the control functions are composed of the metric in the triangle inequality, where the control functions in a double-controlled metric-type space are multiplied with the metric . We establish some fixed-point theorems along with the examples and applications.- 14 April 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (8) , 1866
Open AccessDouble-Composed Metric Spaces
The double-controlled metric-type space is a metric space in which the triangle inequality has the form for all . The maps are called control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form for all . In our new space, the control functions are composed of the metric in the triangle inequality, where the control functions in a double-controlled metric-type space are multiplied with the metric . We establish some fixed-point theorems along with the examples and applications.