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A note on the convergence of Phillips operators by the sequence of functions via q-calculus

Kiliçman Adem, Ayman-Mursaleen Mohammad, Nasiruzzaman Md.

Demonstratio Mathematica

2022

Vol. 55, nr 1

615--633

The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.

Korovkin type theorem for sequences of operators depending on a parameter

Finta Z.

Demonstratio Mathematica

2015

Vol. 48, nr 3

391--403

We establish necessary and sufficient conditions for a parameter depending sequence (Ln,λ)n≥1 of positive linear operators such that (Ln,λ)n≥1 converges in the strong operator topology to its limit operator. Some applications of our theorem are also presented.

Approximation by q-Szász-Mirakyan-Baskakov operators

Gupta V., Aral A., Ozhavzali M

Fasciculi Mathematici

2012

Nr 48

35--48

In the present paper we propose the q analogue of well known Szász-Mirakyan-Baskakov operators (see e.g. [14], [7]). We apply q-derivatives, and q-Beta functions to obtain the moments of the q-Szász-Mirakyan-Baskakov operators. Here we estimate some direct approximation results for these operators.