Hanan Darwish

The use of integral and differential operators in geometric function theory has continued to gain interest among researchers in the field of study in recent times. This is due to the wide range of its applications in science, technology and engineering. In this work, therefore, the authors defined and investigated a new subclass of analytic functions in the open unit disk using the $\mathfrak{q}$-Srivastava–Attiya convolution operator and the Jackson’s $\mathfrak{q}$-derivative, by means of the subordination. The authors used two well-known lemmas to determine a sharp upper-bound for the Fekete–Szeg$\ddot{o}$ functional in two different cases. In particular, the authors introduced a new generalized subclass of complex order univalent functions denoted by ${\mathcal{L}}_{\mathfrak{q},\mathfrak{b},\mathfrak{h}}^{\mathfrak{s}}\left(\tau ,,,\Phi \right)$ and derived the coefficient estimates $a_{\iota }(\iota =2,3)$ of the Taylor–Maclaurin series in this class, as well as the Fekete–Szeg$\ddot{o}$ inequality $\left|a_3,-,\aleph ,a_2^2\right|$ for functions in this class. The work generalizes many known results in the literature.

In this paper, we introduce and investigate a new subclass ${\left({\mathcal{R}}_{\varsigma }^u\right)}^{\mathfrak{g}}\left(\varphi \right)$ of universally prestarlike generalized functions of order $\varsigma$, where $\varsigma \le 1$, associated with a shell-shaped region defined by $\Lambda =\mathrm{C}\setminus [1,\infty )$ for the present investigation, by utilizing the Srivastava–Owa fractional derivative of order $\delta$. Coefficient inequalities for $|{\mathfrak{a}}_2|$ and $|{\mathfrak{a}}_3|$ for functions belonging to the newly introduced class are obtained. Additionally, the Fekete–Szegö inequality is investigated for this class of functions. In order to enhance the coefficient studies for this class, the second Hankel determinant is also evaluated.

In the present paper, we propose new generalized classes of (p,q)-starlike and (p,q)-convex functions. These classes are introduced by making use of a (p,q)-derivative operator. There are established Fekete–Szegö estimates $|a_3-\mu a_2^2|$ for functions belonging to the newly introduced subclasses. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined.

Certain characteristics of univalent functions with negative coefficients of the form $f\left(z\right)=z-{\sum }_{n=1}^{\infty }{a}_{2n}{z}^{2n},a_{2n}>0$ have been studied by Silverman and Berman. Pokley, Patil and Shrigan have discovered some insights into the Hadamard product of $\mathcal{P}$-valent functions with negative coefficients. S. M. Khairnar and Meena More have obtained coefficient limits and convolution results for univalent functions lacking a alternating type coefficient. In this paper, using the $\mathfrak{q}$-Difference operator, we developed the a subclass of meromorphically $\mathcal{P}$-valent functions with alternating coefficients. Additionally, we obtained multivalent function convolution results and coefficient limits.

This work presents a novel investigation that utilizes the integral operator $I_{p,\lambda }^n$ in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered.

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc $D^{*}=\{z\in \mathbb{C}:0<|z|<1\}$ that includes fixed second coefficients of class $\mathcal{A}{}_{s,c}^d\left(\psi ,\tau ,\nu ,\eta \right)$ and the q- hypergeometric functions. For the function belonging to the class $\mathcal{A}{}_{s,c}^d\left(\psi ,\tau ,\nu ,\eta \right),$ some properties are obtained, including the coefficient inequalities, closure theorems, and the radius of convexity.

Prostate cancer is a significant cause of morbidity and mortality in the USA. In this paper, we develop a computer-aided diagnostic (CAD) system for automated grade groups (GG) classification using digitized prostate biopsy specimens (PBSs). Our CAD system aims to firstly classify the Gleason pattern (GP), and then identifies the Gleason score (GS) and GG. The GP classification pipeline is based on a pyramidal deep learning system that utilizes three convolution neural networks (CNN) to produce both patch- and pixel-wise classifications. The analysis starts with sequential preprocessing steps that include a histogram equalization step to adjust intensity values, followed by a PBSs’ edge enhancement. The digitized PBSs are then divided into overlapping patches with the three sizes: 100 × 100 ($CN{N}_S$), 150 × 150 ($CN{N}_M$), and 200 × 200 ($CN{N}_L$), pixels, and 75% overlap. Those three sizes of patches represent the three pyramidal levels. This pyramidal technique allows us to extract rich information, such as that the larger patches give more global information, while the small patches provide local details. After that, the patch-wise technique assigns each overlapped patch a label as GP categories (1 to 5). Then, the majority voting is the core approach for getting the pixel-wise classification that is used to get a single label for each overlapped pixel. The results after applying those techniques are three images of the same size as the original, and each pixel has a single label. We utilized the majority voting technique again on those three images to obtain only one. The proposed framework is trained, validated, and tested on 608 whole slide images (WSIs) of the digitized PBSs. The overall diagnostic accuracy is evaluated using several metrics: precision, recall, F1-score, accuracy, macro-averaged, and weighted-averaged. The ($CN{N}_L$) has the best accuracy results for patch classification among the three CNNs, and its classification accuracy is 0.76. The macro-averaged and weighted-average metrics are found to be around 0.70–0.77. For GG, our CAD results are about 80% for precision, and between 60% to 80% for recall and F1-score, respectively. Also, it is around 94% for accuracy and NPV. To highlight our CAD systems’ results, we used the standard ResNet50 and VGG-16 to compare our CNN’s patch-wise classification results. As well, we compared the GG’s results with that of the previous work.