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Quantitative estimations of bivariate summation‐integral–type operators
Author(s) -
Yadav Rishikesh,
Meher Ramakanta,
Mishra Vishnu Narayan
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5824
Subject(s) - mathematics , bivariate analysis , polynomial , bounded function , function (biology) , convergence (economics) , weight function , partial derivative , bounded variation , type (biology) , uniform convergence , mathematical analysis , statistics , ecology , evolutionary biology , economics , biology , economic growth , computer network , bandwidth (computing) , computer science
In this paper, we study the approximation properties of bivariate summation‐integral–type operators with two parameters m , n ∈ N . The present work deals within the polynomial weight space. The rate of convergence is obtained while the function belonging to the set of all continuous and bounded function defined on ([0], ∞ )(×[0], ∞ ) and function belonging to the polynomial weight space with two parameters, also convergence properties, are studied. To know the asymptotic behavior of the proposed bivariate operators, we prove the Voronovskaya type theorem and show the graphical representation for the convergence of the bivariate operators, which is illustrated by graphics using Mathematica. Also with the help of Mathematica, we discuss the comparison by means of the convergence of the proposed bivariate summation‐integral–type operators and Szász‐Mirakjan‐Kantorovich operators for function of two variables with two parameters to the function. In the same direction, we compute the absolute numerical error for the bivariate operators by using Mathematica and is illustrated by tables and also the comparison takes place of the proposed bivariate operators with the bivariate Szász‐Mirakjan operators in the sense of absolute error, which is represented by table. At last, we study the simultaneous approximation for the first‐order partial derivative of the function.