On [Formula: see text]-Szász-Mirakyan operators and their approximation properties

M Mursaleen; Aah Al-Abied; Abdullah Alotaibi

doi:10.1186/s13660-017-1467-z

On [Formula: see text]-Szász-Mirakyan operators and their approximation properties

J Inequal Appl. 2017;2017(1):196. doi: 10.1186/s13660-017-1467-z. Epub 2017 Aug 24.

Authors

M Mursaleen^{1

2}, Aah Al-Abied¹, Abdullah Alotaibi²

Affiliations

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

Abstract

In the present paper, we introduce a new modification of Szász-Mirakyan operators based on [Formula: see text]-integers and investigate their approximation properties. We obtain weighted approximation and Voronovskaya-type theorem for new operators.

Keywords: Voronovskaya theorem; [Formula: see text]-Szász-Mirakyan operators; [Formula: see text]-integers; q-Szász-Mirakyan operators; q-integers; weighted approximation.