Approximation of GBS Type q-Jakimovski-Leviatan-Beta Integral Operators in Bögel Space

Abdullah Alotaibi

doi:10.3390/math10050675

Abstract

In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS form for these new operators and then study the degree of approximation by means of modulus of smoothness, mixed modulus of smoothness and Lipschitz class of Bögel continuous functions.

Highlights

Introduction and PreliminariesIn 1950, very famous mathematician, Szász, introduced the operators known as Szász positive linear operators [1]
Take M2 = {(v1, v2 ) : 0 ≤ v1 < ∞, 0 ≤ v2 < ∞}, and C M2 is the class of all continuous functions on M2 and satisfies the norm by || g||C(M2 ) = sup(v1,v2 )∈M2 | f (v1, v2 )|
Bögel functions and GBS-type operators related to this paper, we propose the article [33,34,35,36,37,38]

Summary

Introduction and Preliminaries

In 1950, very famous mathematician, Szász, introduced the operators known as Szász positive linear operators [1]. Suppose v ∈ [0, ∞) and the class of all continuous functions on [0, ∞) is C [0, ∞), for all f ∈ C [0, ∞), the Szász operators are defined as: Citation: Alotaibi, A. For more related concepts on these classes of functions, we prefer to see the recent published article by Nasiruzzaman et al [14,15,16,17,18,19]. There are various operators in several functional spaces given by the authors: Mohiuddine et al [20,21,22,23], Mursaleen et al [24,25], Acar et al [26], Kajla et al [27], Özger et al [28], and Rao et al [29,30]

Operators and Their Associated Moments

Approximation in Weighted Space and Degree of Convergence

GBS-Type Approximation in Bögel Space

Conclusions