In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family ${\mathcal{SW}}_{\Sigma }(\delta ,\gamma ,\lambda ,\mathfrak{s},\mathfrak{t},q,r)$ of normalized holomorphic and bi-univalent functions in the open unit disk $\mathbb{U}$, which are associated with the Bazilevič functions and the $\lambda$-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family ${\mathcal{SW}}_{\Sigma }(\delta ,\gamma ,\lambda ,\mathfrak{s},\mathfrak{t},q,r)$. Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function $\Phi (z,s,a)$ is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself.

Recently, Srivastava et al. introduced and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Our principal objective in thi

Let ${\mathcal{S}}_s^{*}$ be the class of normalized functions f defined in the open unit disk $\mathbb{D}=\{z:|z|<1\}$ such that the quantity $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}$ lies in an eight-shaped region in the right-half plane and satisfying the condition $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}\prec 1+sinz(z\in \mathbb{D}).$ In this paper, we aim to investigate the third-order Hankel determinant $H_3\left(1\right)$ and Toeplitz determinant $T_3\left(2\right)$ for this function class ${\mathcal{S}}_s^{*}$ associated with sine function and obtain the upper bounds of the determinants $H_3\left(1\right)$ and $T_3\left(2\right)$ .

This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown.

In this paper, we have established some fixed point theorems in the context of strong b-metric spaces. For this purpose, Ciric type contraction for single-valued mapping and Nadler’s type Banach and Chatterjea contractions for set-valued mappings are applied to obtain fixed point and common fixed points. A simple and different technique has been used to obtain the results. Our results unify, extend and generalize the existence of corresponding present and conventional results existing in the literature of fixed point theory.

A class of p-valent analytic functions is introduced using the q-difference operator and the familiar Janowski functions. Several properties of functions in the class, such as the Fekete–Szegö inequality, coefficient estimates, necessary and sufficient conditions, distortion and growth theorems, radii of convexity and starlikeness, closure theorems and partial sums, are discussed in this paper.