On a New Class of Bernstein Type Operators Based on Beta Function

Document Type : Original Article

Authors

Dhawal J. Bhatt ¹

Vishnu Narayan Mishra ²

Ranjan Kumar Jana ¹

¹ Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395 007 (Gujarat), India.

² Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, (Madhya Pradesh)- 484 887, India.

10.22034/kjm.2019.97090

Abstract

We develop Bernstein type operators using the Beta function and study their approximation properties. By using Korovkin's theorem, we achieve the uniform convergence of sequences of these operators. We obtain the rate of convergence in terms of modulus of continuity and establish the Voronovskaja type asymptotic result for these operators. At last the graphical comparison of these newly defined operators with few of the fundamental but significant operators is discussed.

Keywords

Beta function

Korovkin theorem

modulus of continuity

Voronovskaya type result

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