Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators

Abstract

In this paper, the study of the problem of simultaneous approximation by the Szász-Mirakjan-Stancu-Durrmeyer type operators is carried out. An upper bound for the approximation to the r th-derivative of a function by these operators is established.

Local and global results for modified Szász–Mirakjan operators

“… introduced Szász–Mirakjan–Durrmeyer‐type generalization given by where is an increasing sequence of positive real numbers, b n → ∞ as n → ∞ , b 1 ≥1 and studied the simultaneous approximation properties of the operators . References contain some more work in this direction.…”

“…1, b 1 1 and studied the simultaneous approximation properties of the operators (1). References [2][3][4] contain some more work in this direction.…”

Approximation by modified Jain-Baskakov-Stancu operators

“…As a special case, i.e., c = 1, the operators (1.1) reduced in Jain-Baskakov operators which is defined in [32]. In [28], Stancu introduced the positive linear operators P Motivated by his work, the Stancu type modification of many sequences of linear positive operators has been considered and studied (see [1], [7], [15], [17] [32], [34] For α = γ = 0, we denote K α,γ n,c,β (f ; x) by K β n,c (f ; x). The aim of this paper is to study the basic convergence theorem, Voronovskaja type asymptotic result, rate of convergence, weighted approximation and pointwise estimation of the operators (1.4).…”

A summation‐integral type modification of Szász–Mirakjan operators

“…The operators, their modifications and generalizations are studied extensively for the properties like global approximation in polynomial and exponential weight spaces, uniform approximation, simultaneous approximation. We can mention some important studies of this type , , , , , ). There are summation integral type modification of operators of the form (, like appeared in literature .…”