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2023, Volume 6, Issue 4: 651-669. Doi: 10.3934/mfc.2022037

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Dunkl analouge of Sz$ \acute{a} $sz Schurer Beta bivariate operators

1.
Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, 484887, India
2.
Department of Applied Sciences and Humanities, Panipat, Institute of Engineering and Technology, Pattikalyana, Samalkha, Panipat-132102, India; Current address: Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali-140243, Punjab, India

^*Corresponding authors: Mohd Raiz and Vishnu Narayan Mishra
^*Corresponding authors: Mohd Raiz and Vishnu Narayan Mishra

Received: April 2022

Revised: September 2022

Early access: September 2022

Published: November 2023

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Abstract

The motive of this research article is to introduce a sequence of Sz$ \acute{a}sz $ Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in B$ \ddot{o} $gel space via mixed modulus of continuity.

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Mathematics Subject Classification: Primary: 41A10, 41A25, 41A36; Secondary: 41A63.

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