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Journal of Function Spaces
Volume 2016 (2016), Article ID 1035253, 9 pages
http://dx.doi.org/10.1155/2016/1035253
Research Article

On a Kantorovich Variant of -Szász-Mirakjan Operators

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 23 October 2015; Accepted 31 December 2015

Academic Editor: Pasquale Vetro

Copyright © 2016 M. Mursaleen 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

We propose a Kantorovich variant of -analogue of Szász-Mirakjan operators. We establish the moments of the operators with the help of a recurrence relation that we have derived and then prove the basic convergence theorem. Next, the local approximation and weighted approximation properties of these new operators in terms of modulus of continuity are studied.