In this article, a new generalized $ q $-Mittag-Leffler function is introduced and investigated. Motivated by the newly defined function and using the concept of differential subordination, a new subclass of multivalent functions is introduced. Some geometric properties of them are obtained. Furthermore, the radii for the aforementioned subclass associated with a generalized Srivastava-Attiya integral operator are also studied.

Ma-Minda-type analytic functions have been a central topic in geometric function theory due to their importance in studying properties such as univalence, convexity, and starlikeness. However, the class of Ma-Minda functions associated with kidney-shaped domains has not been systematically investigated before, leaving a clear research gap. In this paper, we introduced and studied the geometric properties of class $ {\mathcal{S}}^*_k $. Our approach combined rigorous geometric analysis with Python programming (version 3.13.2) and graphical illustrations, providing both theoretical depth and computational support. Several inclusion relations and radius problems for $ {\mathcal{S}}^*_k $ were established in comparison with other known classes. Furthermore, we examined various problems related to the initial coefficient bounds, with particular emphasis on their sharpness.

In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevič functions, denoted as ${\mathcal{T}}_{q,\tau +1,u}^{\mu }(\vartheta ,\lambda ,\mathcal{M},\mathcal{N})$. Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory.

The purpose of this study is to present the idea of an f-partition for a closed interval. Additionally, we introduce a new notion for fuzzy cone metric spaces called a fuzzy cone integrable function and prove fundamental fixed-point theorems. Moreover, we develop the concept of a ξ -fuzzy cone integrable function. Finally, we present new results of the fixed- point theorem for ξ -fuzzy cone integrable functions.