Approximation properties of Chlodowsky variant of [Formula: see text] Bernstein-Stancu-Schurer operators

Vishnu Narayan Mishra; M Mursaleen; Shikha Pandey; Abdullah Alotaibi

doi:10.1186/s13660-017-1451-7

Approximation properties of Chlodowsky variant of [Formula: see text] Bernstein-Stancu-Schurer operators

J Inequal Appl. 2017;2017(1):176. doi: 10.1186/s13660-017-1451-7. Epub 2017 Aug 1.

Authors

Vishnu Narayan Mishra^{1

2}, M Mursaleen³, Shikha Pandey⁴, Abdullah Alotaibi⁵

Affiliations

¹ Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887 India.
² L. 1627 Awadh Puri Colony, Phase-III, Beniganj, Opposite-Industrial Training Institute (I.T.I.), Ayodhya Main Road, Faizabad, Uttar Pradesh 224001 India.
³ Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
⁴ Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat 395007 India.
⁵ Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.

Abstract

In the present paper, we introduce the Chlodowsky variant of [Formula: see text] Bernstein-Stancu-Schurer operators which is a generalization of [Formula: see text] Bernstein-Stancu-Schurer operators. We also discuss its Korovkin-type approximation properties and rate of convergence.

Keywords: [Formula: see text]-Bernstein operators; [Formula: see text]-integers; linear positive operators.