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ON STANCU TYPE GENERALIZATION OF (p, q)-SZÁSZ-MIRAKYAN KANTOROVICH TYPE OPERATORS
MISHRA, VISHNU NARAYAN,DEVDHARA, ANKITA R The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.3
In this article, we present the Stancu generalization of (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type linear positive operators. Using Korovkin's result, approximation properties are investigated. First, we evaluate moments and direct results. By choosing p and q, the convergence rate have been estimated for better approximation. For the particular case ${\alpha}=0$, ${\beta}=0$ we obtain results for (p, q)-$Sz{\acute{a}}sz$-Mirakyan Kantorovich type operators.
ON STANCU TYPE GENERALIZATION OF (p; q)-SZASZ-MIRAKYAN KANTOROVICH TYPE OPERATORS
Vishnu Narayan Mishra,Ankita R Devdhara 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.3
In this article, we present the Stancu generalization of $(p,q)$-Sz$\acute{a}$sz-Mirakyan Kantorovich type linear positive operators. Using Korovkin's result, approximation properties are investigated. First, we evaluate moments and direct results. By choosing $p$ and $q$, the convergence rate have been estimated for better approximation. For the particular case $\alpha=0, \beta=0$ we obtain results for $(p,q)$-Sz$\acute{a}$sz-Mirakyan Kantorovich type operators.
Some approximation properties of modified Szasz-Mirakjan-Baskakov operators
Prashantkumar patel,Vishnu Narayan Mishra 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.3
The generalization of well known Száasz-Mirakjan operators was introduction by G C Jain, Approximation of functions by a new class of linear operators, Journal of the Australian Mathematical Society, 13(3):271-276, 1972. In P Patel and V N Mishra, Jain-Baskakov op- erators and its different generalization, Acta Mathematica Vietnamica, 40:715-733, 2015 introduced the integral modification of Jain operators and discussed its different generalization. In this manuscript, we extend the study of the operators introduced by Patel & Mishra and discussed some direct results in ordinary approximation for this operators. The generalization of well known Szász-Mirakjan operators was introduction by G C Jain, Approximation of functions by a new class of linear operators, Journal of the Australian Mathematical Society, 13(3):271-276, 1972. In P Patel and V N Mishra, Jain-Baskakov op- erators and its different generalization, Acta Mathematica Vietnamica, 40:715-733, 2015 introduced the integral modification of Jain operators and discussed its different generalization. In this manuscript, we extend the study of the operators introduced by Patel & Mishra and discussed some direct results in ordinary approximation for this operators.
Pragati Gautam,VISHNU NARAYAN MISHRA,Komal Negi 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.2
In this paper, we prove the existence and uniqueness of common fixed point for \'Ciri\'c-Riech-Rus contraction mapping in the setting of quasi-partial $\it{b}$-metric space. Some examples are given to verify the effectiveness of our results.
THE CERTAIN SUMMATION INTEGRAL TYPE OPERATORS AND ITS INVERSE THEOREM
PRASHANTKUMAR PATEL,VISHNU NARAYAN MISHRA 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.2
In [1], Patel and Mishra introduced and discussed Stancu type generalization of integral modification of the well-known Baskakov operators with the weight function of Beta basis function. Simultaneous approximation results of these operators were established by Patel and Mishra [2]. The present paper deals with detail proof of inverse theorem of these operators.
SOME WEIGHTED APPROXIMATION PROPERTIES OF NONLINEAR DOUBLE INTEGRAL OPERATORS
Uysal, Gumrah,Mishra, Vishnu Narayan,Serenbay, Sevilay Kirci The Kangwon-Kyungki Mathematical Society 2018 한국수학논문집 Vol.26 No.3
In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.
A GENERIC RESEARCH ON NONLINEAR NON-CONVOLUTION TYPE SINGULAR INTEGRAL OPERATORS
Uysal, Gumrah,Mishra, Vishnu Narayan,Guller, Ozge Ozalp,Ibikli, Ertan The Kangwon-Kyungki Mathematical Society 2016 한국수학논문집 Vol.24 No.3
In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = <a, b> and ${\Omega}$ = <A, B> stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.
Safeer Hussain Khan,Ritika,Vishnu Narayan Mishra 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.1
CAT(0) spaces contain a number of spaces including both linear and nonlinear ones. The class of generalized asymptotically quasi-nonexpansive mappings is a very wide class of mappings. Iterative processes are used to approximate solutions when actual one is hard to find. In this paper, we prove strong convergence results using a three step iterative process for generalized asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Our results remain valid in both linear and nonlinear domains. Thus our results generalize the corresponding results of many authors.
Solvability of some non-linear functional integral equations via measure of noncompactness
Deepak Dhiman,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.2
In this study, we establish some results related to the existence of solutions for nonlinear functional integral equations, by Darbo's fixed point theorem in Banach algebra, which contains several functional integral equations that arise in mathematical analysis. As an application, we also provide an example of functional integral equations.
Some properties of bilinear mappings on the tensor product of $C^*$-algebras
Anamika Sarma,Nilakshi Goswami,Vishnu Narayan Mishra 강원경기수학회 2019 한국수학논문집 Vol.27 No.4
Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras and $\mathcal{A}\otimes\mathcal{B}$ be their algebraic tensor product. For two bilinear maps on $\mathcal{A}$ and $\mathcal{B}$ with some specific conditions, we derive a bilinear map on $\mathcal{A}\otimes\mathcal{B}$ and study some characteristics. Considering two $\mathcal{A}\otimes\mathcal{B}$ bimodules, a centralizer is also obtained for $\mathcal{A}\otimes\mathcal{B}$ corresponding to the given bilinear maps on $\mathcal{A}$ and $\mathcal{B}$. A relationship between orthogonal complements of subspaces of $\mathcal{A}$ and $\mathcal{B}$ and their tensor product is also deduced with suitable example.