Approximation Properties of Modified Baskakov Gamma Operators

Abstract

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.

Matrix Transforms of Speed-Summable and Speed-Bounded Sequences

“…We note that the results connected with convergence, absolute convergence, boundedness, A λ -boundedness and A λ -summability with speed can be used in several applications, for example in the approximation theory. Besides, one author of the present paper used such results for the estimation of the order of approximation of Fourier expansions in Banach spaces ([7] - [9], [11]).…”

Approximation by modified q‐Gamma type operators in a polynomial weighted space

“…For instance, Acar et al 15 constructed a new sequence of Gamma type operators which preserves the exponential functions $$$ {e}^{k\omega x},k=1,2 $$$ and studied the rate of convergence by means of an appropriate modulus of continuity and a Voronovskaja type asymptotic result in weighted approximation. Arpaguş and Olgun 16 investigated the rate of approximation of modified Baskakov–Gamma operators and also discussed a Voronovskaja type theorem in weighted approximation by these operators. Artee 17 presented a modified form of the general Gamma type operators and derived some direct results for bounded functions on $$$ \left[0,\infty \right) $$$ and a Korovkin type theorem for functions in a weighted space.…”

Approximation properties of modified Jain-Gamma operators

“…e −xy y n F p x, n y dy and investigated the approximation properties for differentiable functions in the polynomial weighted spaces. Recently, new operators have been defined by using the Gamma operator and the convergence properties of these operators are examined [1,6,10,21].…”