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Journal of Function Spaces
Volume 2019, Article ID 2329060, 12 pages
https://doi.org/10.1155/2019/2329060
Review Article

On Sequences of J. P. King-Type Operators

1Department of Mathematics, Faculty of Science, Selcuk University, Selcuklu, Konya, Turkey
2Department of Mathematics, University of Bari, Bari, Italy
3Department of Mathematics, University of Jaén, Jaén, Spain
4Department of Mathematics, Computer Science and Economics, University of Basilicata, Potenza, Italy

Correspondence should be addressed to Vita Leonessa; ti.sabinu@assenoel.ativ

Received 28 February 2019; Accepted 2 May 2019; Published 16 May 2019

Academic Editor: Guozhen Lu

Copyright © 2019 Tuncer Acar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and on . Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King’s approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators.