Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47886120200101On a New Class of Bernstein Type Operators Based on Beta Function1159709010.22034/kjm.2019.97090ENDhawal J.BhattApplied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395
007 (Gujarat), India.Vishnu NarayanMishraDepartment of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, (Madhya Pradesh)- 484 887, India.0000-0002-2159-7710Ranjan KumarJanaApplied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395
007 (Gujarat), India.Journal Article20190415We 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.http://www.kjm-math.org/article_97090_cadb0c8d0798a9820fa3976ce509413e.pdf