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Statistical Summability of Double Sequences by the Weighted Mean and Associated Approximation Results

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Book cover Applied Mathematical Analysis: Theory, Methods, and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 177))

Abstract

The goal of this chapter is to extend various summability concepts and summability techniques by the weighted mean method with respect to the generalized difference operator involving (p, q)-Gamma function. We also obtain some inclusion relations between newly proposed methods and present some illustrative examples to show that these non-trivial generalizations are more powerfull than the existing literature on this topic. Furthermore, some approximation theorems and their weighted statistical forms for functions of two variables are proved. As application, related approximation results associated with the (p, q)-analogue of generalized bivariate Bleimann-Butzer-Hahn operators are derived. Finally, we estimate the rate of convergence of approximating positive linear operators in terms of the modulus of continuity.

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Authors and Affiliations

  1. Institute of Natural And Applied Sciences, Gazi University, TR-06500, Ankara, Turkey

    Uğur Kadak

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  1. Uğur Kadak
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Correspondence to Uğur Kadak .

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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

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Kadak, U. (2020). Statistical Summability of Double Sequences by the Weighted Mean and Associated Approximation Results. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-99918-0_3

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