In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations ...

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. Recently the statistical convergence of Bernstein operators was studied. In this ...

In this note we present a Kantorovich variant of the operators proposed by [X. Y. Chen, J. Q. Tan, Z. Liu, J. Xie, J. Math. Anal. Appl., 450 (2017), 244-261] based on non-negative parameters. Here, we prove an approximation ...

We present here a further investigation for the classical Frobenius-Euler polynomials. By making use of the generating function methods and summation transform techniques, we establish some summation formulas for the ...

In the present paper, we introduce a method in order to obtain some new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial basis. Finally, ...

In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...

We introduce Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-invairant integral in the p-adic integer ring and obtain some new interesting identities. Using a complex contour integral representation ...

The present paper introduces the Szasz-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. ...

In the paper, using the extended fermionic p-adic integral on Z(p), the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and ...

The aim of this paper is to introduce new notion of generalized (alpha, psi)-expansive mappings in generalized metric spaces and to study the existence of a fixed point for the mappings in this space. Our new notion ...