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Numerical Analysis and Applications

2022 year, number 2

Approximation properties by some modified Szasz-Mirakjan-Kantorovich operators

Rishikesh Yadav1, Ramakanta Meher1, Vishnu Narayan Mishra2
1Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology Surat, Gujarat,India
2Department of Mathematics, Indira Gandhi National Tribal University, Madhya Pradesh, India
Keywords: rate of convergence, Lipschitz function, Ditzian-Totik modulus of smoothness, function of bounded variation


The present article deals with approximation results by means of the Lipschitz maximal function, Ditzian-Totik modulus of smoothness, and Lipschitz type space having two parameters for the summation-integral type operators defined by Mishra and Yadav [22]. Further, we determine the rate of convergence in terms of the derivative of bounded variation. To estimate the quantitative results of the defined operators, we establish quantitative Voronovskaya type and Gruss type theorems. Moreover; examples are given with graphical representation to support the main results.