Approximation of Modified Jakimovski-Leviatan-Beta Type Operators

Abstract

In the present paper, we define Jakimovski-Leviatan type modified operators. We study some approximation results for these operators. We also determine the order of convergence in terms of modulus of continuity, Lipschitz functions, Peetre's K-functional, second order modulus of continuity and weighted modulus of continuity.

Rate of Approximation for Modified Lupaş-Jain-Beta Operators

“…As we know, in order to approximate Lebesgue integrable functions, the most important modifications are Kantorovich and Durrmeyer integral operators. Motivated by the above mentioned Durrmeyer type generalizations of various operators and also from [11][12][13][14][15][16][17][18][19][20][21][22][23], in this paper, Durrmeyer-type modification of generalized Lupaş-Jain operators (5) by taking weights of some beta basis function is defined as follows:…”

Dunkl-type generalization of the second kind beta operators via $(p,q)$-calculus

“…In this section we construct a class of (p, q)-variant of Szász-Beta operators of the second kind generated by an exponential function via Dunkl generalization in Definition 2.1. Such operators are a generalized version of the operators studied in [7,22,28,29,31,36,45].…”

New Generating Function Relations for the q-Generalized Cesàro Polynomials

“…In addition, the basic functions of a variable that can be expressed in terms of (⋅) functions can be found in the works of Yadav and Purohit [13,14]. In the last quarter of the twentieth century, the quantum calculus (also known as −calculus) can be found on the theory of approaches of operators [15,16].…”