In the field of geometric function theory, we use the ( p , q )‐differential operator in the complex unit disk to describe a novel class of symmetrical starlike functions of order η . Several interesting properties of functions belonging to the class are examined, such as growth, distortion, and convolution characteristics.

In the present article, an emerging subdivision‐based technique is developed for the numerical solution of linear Volterra partial integrodifferential equations (LVPIDEs) of order four with a weakly singular kernel. To approximate the spatial derivatives, the basis function of the subdivision scheme is used, whereas the time discretization is done with the backward Euler method (BEM), and the product trapezoidal rule has been used for the approximation of the integral term. To check the numerical and graphical efficiency of the proposed algorithm, many test problems have been considered. The numerical and visual results confirm the numerical efficiency and robustness of our technique.

In 1990, Ismail et al. introduced a generalized class of starlike functions using the q ‐derivative operator. Similarly, many authors have studied various subclasses of analytic functions involving the q ‐derivative operator from different perspectives. This paper is aimed at presenting new subclasses of analytic and spiral‐like functions related to the Janowski function, defined by the q ‐derivative operator. Convolution characterizations, coefficient conditions, and other properties of these classes are also derived. Additionally, we discuss special cases and some useful corollaries of our main results.

In this paper, we introduce a class of functions associated with Hölder’s inequality and show the Schur convexities of these functions. With the help of Schur convexity, several improved versions of Hölder’s inequality are established. The results obtained here are the generalizations and refinements of the existing results for Hölder’s inequality. At the end of the paper, we provide an application of the present result to the improvement of Minkowski’s inequality.

Two‐analytic weighted Bergman space is a nonanalytic function space which is closely related to analytic functions. In this paper, we mainly discuss the zero product problem for Toeplitz operators on the 2‐analytic weighted Bergman space.

Geometric function theory (GFT) is the study of geometric properties of analytic functions. The cornerstone of GFT is the theory of univalent functions. Several related topics in GFT with various applications have been developed over the years, one of which includes the study of special functions. In particular, the sigmoid function in relation to GFT is being investigated. However, the connection between the modified sigmoid function and the β ‐ Catas differential operator is yet to be studied. In this paper, a new class of analytic function is defined using the Sigmoid β− Catas operator. The corresponding coefficient bounds, Fekete–Szego functional, and second order and third order Hankel determinants were determined by the principle of subordination. Furthermore, the second order and third order Toeplitz determinants for this class were also obtained.

In this article, we present new results addressing the fixed‐circle and fixed‐disc problems through modification of the multivalued bilateral Jaggi‐type and Dass–Gupta‐type contractions. Furthermore, we demonstrate the application of these theorems to the nonlinear activation mechanism used in neural networks. These mechanisms introduce nonlinearity and deep learning models to learn effectively and to represent complex patterns.

Let be the Hilbert–Schmidt class on a complex separable Hilbert space . In light of the recent definition of the weighted numerical radius and motivated by the definition of the Hilbert–Schmidt numerical radius of a pair of operators, we introduce the definition of the weighted Hilbert–Schmidt numerical radius of a pair of operators. This definition involves a pair of weights and can be stated as follows: where and 0 ≤ v, μ ≤ 1. We prove that ω2,v,μ(A, B) defines a norm on . Motivated by this definition, we refine, generalize, and obtain some well‐known Hilbert–Schmidt numerical radius inequalities that appear in many recent papers in this direction. Also, we present some new lower and upper bounds for ω2,v,μ(·, ·).

The aim of this paper is to obtain the sufficient and necessary conditions for weighted composition operators uCφ with φ(z) = az + b (|a| ≤ 1), , where a, b, c, d ∈ ℂ, to be binormal or quasinormal on the Fock space . Surprisingly, the normality, quasinormality, and binormality of the above weighted composition operators uCφ are equivalent for |a| < 1; however, there exist non‐normal binormal weighted composition operators for |a| = 1.

In this article, we study the existence and uniqueness of fixed points for mappings in Kaleva–Seikkala’s type fuzzy b‐metric spaces. Nonlinear contractions of the comparison function and Boyd–Wong’s type are considered, and several new fixed point theorems for these contractions in complete Kaleva‐Seikkala’s type fuzzy b‐metric spaces are presented. It is remarkable that the contractive conditions of our results do not depend on the space coefficient b. The presented work extends and improves some well‐known results in the literature. Finally, as an application, we demonstrate a unique solution to both the Fredholm integral equation and the fractional differential equation.