The purpose of this paper is to construct a general class of operators which has known Baskakov-Szász-Stancu that preserving constant and e 2ax , a > 0 functions. We scrutinize a uniform convergence result and analyze the asymptotic behavior of our operators, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Szász-Stancu operators and the recent operators.

Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol Diaz et al. 2017, which are one of the vital generalizations of hypergeometric functions. We introduce k-analogues of F2and F3 Appell functions denoted by the symbols F2,kand F3,k,respectively, just like Mubeen et al. did for F1 in 2015. Meanwhile, we prove integral representations of the k-generalizations of F2and F3 which provide us with an opportunity to generalize widely used identities for Appell hypergeometric functions. In addition, we present some important transformation formulas and some reduction formulas which show close relation not only with k-Appell functions but also with k-hypergeometric functions. Finally, employing the theory of Riemann–Liouville k-fractional derivative from Rahman et al. 2020, and using the relations which we consider in this paper, we acquire linear and bilinear generating relations for k-analogue of hypergeometric functions and Appell functions.

In this paper, we present a family of multivariable polynomials defined by Rodrigues formula and we discuss their some miscellaneous properties such as generating function and recurrence relation. We also derive various classes of multilateral generating functions for these multivariable polynomials and give some special cases of the results. Furthermore, we also show that some particular cases of the polynomials reduce to the products of Hermite and Laguerre orthogonal polynomials with one variable.

The goal of this paper is to construct a general class of operators which has known Baskakov-Schurer-Szász that preserving constant and e 2ax , a > 0 functions. Also, we demonstrate the fact that for these operators, moments can be obtained using the concept of moment generating function. Furthermore, we investigate a uniform convergence result and a quantitative estimate in consideration of given operator, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Schurer-Szász operators and the recent sequence, too.

In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions \(e_{0}\) and \(e^{2ax},\ a>0\) fixed. Using the modulus of continuity, we show the uniform convergence of new operators to \(f\). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.