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Vishnu Narayan Mishra

Publications and source records attributed to Vishnu Narayan Mishra.

At least 19 recordsLinked to original sources
arXiv2023

Application of the Bell polynomials for the solution of some differential-algebraic equations

The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are determined by constructing a recurrence relation. To deal with nonlinearity of the problems, the Faà di Bruno's formula containing the partial ordinary Bell polynomials is applied within the differential transform to avoid computation of symbolic derivatives. The error estimation results are presented too. Four concrete problems are studied to show efficiency and reliability of the method. The obtained results are compared to other methods.

math.NA↗
arXiv2020

Approximation of associated GBS operators by Szasz-Mirakjan type operators

In this article, the approximation properties of the Szasz-Mirakjan type operators are studied for the function of two variables, and the rate of convergence of the bivariate operators is determined in terms of total and partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form of the bivariate Szasz-Mirakjan type operators are considered for the function of two variables to find an approximation of B-continuous and B-differentiable function in the Bogel's space. Further, the degree of approximation of the GBS type operators is found in terms of mixed modulus of smoothness and functions belonging to the Lipschitz class as well as a pioneering result is obtained in terms of Peetre K-functional. Finally, the rate of convergence of the bivariate Szasz-Mirakjan type operators and the associated GBS type operators are examined through graphical representation for the finite and infinite sum which shows that the rate of convergence of the associated GBS type operators is better than the bivariate Szasz-Mirakjan type operators.

math.FA↗
arXiv2020

A study on summation-integral type operators

In this paper, we investigate the approximation properties of the summation-integral type operators as defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8:297-305) and determine the local results as well as prove the convergence theorem of the defined operators. Further, check the asymptotic behavior of the operators and obtain the asymptotic formula for the operators, moreover, the quantitative means of Voronovskaja type theorem is also discussed for an upper bound of the pointwise convergent, as well as obtain the Gruss Voronovskaya-type theorem. Finally, the graphical representation is given to support the approximation results of the operators.

math.FA↗
arXiv2020

Further approximations of Durrmeyer modification of Szasz-Mirakjan operators

The main purpose of this paper is to determine the approximations of Durrmeyer modification of Szasz-Mirakjan operators, defined by Mishra et al. (Boll. Unione Mat. Ital. (2016) 8(4):297-305). We estimate the order of approximation of the operators for the functions belonging to the different spaces. Here, the rate of convergence of the said operators is established by means of the function with derivative of the bounded variation. At last, the graphical analysis is discussed to support the approximation results of the operators.

math.FA↗
arXiv2020

Construction of Szasz-Mirakjan-type operators which preserve a^x; a > 1

In this paper, we introduce a new type of Szasz-Mirakjan operators, which preserve a^x, a > 1 fixed and x\geq 0. We study uniform convergence of the operators by using some auxiliary results and also error estimation is given. The convergence of said operators are shown and analyzed by graphics, also in the same direction, we find a better rate of convergence than Szasz-Mirakjan operators by analyzing the graphics. Voronovskaya-type theorem is studied and a comparison is shown under a sense of convexity with Szasz- Mirakjan operators. In the last section, a modified sequence is constructed in the space of integral function.

math.FA↗
arXiv2019

Convergence of the summation-integral type operators via statistically

Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of approximation is determined. Also using weight function, the weighted statistical convergence theorem with the help of Korovkin theorem is obtained. The statistical rate of convergence in the terms of modulus of continuity and function belonging to the Lipschitz class is obtained. To support the convergence results of the proposed operators to the function, graphical representations take place and a comparison is shown with Szász-Mirakjan-Kantorovich operators through examples. The last section deals with, a bivariate extension of the proposed operators to study the rate of convergence for the function of two variables, additionally, the convergence of the bivariate operators is shown graphically.

math.FA↗
arXiv2019

Approximation properties by some modified Szasz-Mirakjan-Kantorovich operators

The present article deals with the local approximation results by means of 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 (Tbilisi Mathematical Journal. 11(3), (2018), 175-91). Further, we determine the rate of convergence in the term of the with derivative of bounded variation and for the quantitative means of the defined operators, we establish the quantitative Voronovskaya type and Gr$\ddot{\text{u}}$ss type theorems. Moreover, the examples are given with graphical representation to support the main results.

math.FA↗
arXiv2019

Approximation on Durrmeyer modification of generalized Szasz-Mirakjan operators

This paper deals with the approximations of Durrmeyer type generalization of Szasz-Mirakjan operators. We establish the direct results, quantitative Voronovskaya type theorem, Gruss type theorem, A-statistical convergence, rate of convergence in terms of the function with derivative of bounded variation. At last, the graphical analysis, comparison study and numerical representations of proposed operators are discussed.

math.FA↗
arXiv2019

Results on bivariate Szasz-Mirakyan type operators in polynomial weight spaces

In this paper, bivariate Szasz-Mirakjan type operators are introduced along with the estimation of its approximation properties and its rate of convergence. Furthermore, to check the asymptotic behavior of the said bivariate operators, the Voronovskaya type theorem is proved and determined the simultaneous approximation of the operators for first-order partial derivative. Finally, the convergence behavior of the bivariate operators are obtained through graphical representation and validated the numerical results with the results of Szasz-Mirakjan operators for the function of two variables.

math.NA↗
arXiv2019

Study of memory effect in an EOQ model for completely backlogged demand during shortage

The most commonly developed inventory models are the classical economic order quantity model, is governed by the integer order differential equations. We want to come out from the traditional thought i.e. classical order inventory model where the memory phenomena are absent. Here, we want to incorporate the memory effect that is based on the fact economic agents remember the history of changes of exogenous and endogenous variables. In this paper, we have proposed and solved a fractional order EOQ model with constant demand rate where the demand is fully backlogged during shortage time. Finally, a numerical example has been illustrated for this model to show the memory dependency of the system. The numerical example clears that for the considered system the profit is maximum in long memory affected system compared to the low memory affected or memory less system.

math.OC↗
arXiv2018

Iterative Descent Method for Generalized Leontief Model

In this paper we consider generalized Leontief model. We show that under certain condition the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm. We prove the convergence of the method from strictly positive starting point. A numerical example is presented to demonstrate the performance of the algorithm

math.OC↗
arXiv2017

Study of sensitivity of parameters of Bernstein-Stancu operators

This paper is aimed at studying sensitivity of parameters αand βappearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper bound estimation are derived. It is also established that the parameters αand βin Bernstein-Stancu polynomials can be used to get better approximation at a point x = (α)/(β) in [0,1] to the Bernstein polynomials.

math.CA↗
arXiv2016

On Chlodowsky variant of (p,q) Kantorovich-Stancu-Schurer operators

In the present paper, we introduce the Chlodowsky variant of (p,q) Kantorovich-Stancu-Schurer operators on the unbounded domain which is a generalization of (p,q) Bernstein-Stancu-Kantorovich operators. We have also derived its Korovkin type approximation properties and its rate of convergence.

math.CA↗
arXiv2016

Local and global results for modified Szász - Mirakjan operators

In this paper, we study a natural modification of Szász - Mirakjan operators. It is shown by discussing many important established results for Szász - Mirakjan operators. The results do hold for this modification as well, be they local in nature or global, be they qualitative or quantitative. It is also shown that this generalization is meaningful by means of examples and graphical representations.

math.CA↗
arXiv2016

On King Type Modification of $(p,q)$ Baskakov Operators which preserves $x^2$

In the present paper, we construct and investigate a variant of modified $(p,q)$-Baskakov operators, which reproduce the test function $x^2$. The order of approximation of the operators via K-functional and second order, usual modulus of continuity, weighted approximation properties are disscussed. In the end some graphical results, comparison with $(p,q)$-Baskakov operators is explained.

math.CA↗
arXiv2016

(p, q)-Szász-Mirakyan-Baskakov-Stancu type Operators

This deals with the Stancu variant of (p, q)-Szász-Mirakyan-Baskakov operators. Estimation of moments and establishing few basic approximation results which comprise weighted approximation and direct estimates in view of modulus of continuity is the aim of this paper. Steklov mean method has been used for linear approximation. For the particular case α = 0, \b{eta} = 0, we get (p, q) -Szász-Mirakyan-Baskakov operators.

math.CA↗
arXiv2016

On (p, q) Baskakov-Durrmeyer-Stancu Operators

In the present paper, we introduce the generalized form of $(p,q)$ Baskakov-Durrmeyer Operators with Stancu type parameters. We derived the local and global approximation properties of these operators and obtained the convergence rate and behaviour for the Lipschitz functions. Moreover, we give comparisons and some illustrative graphics for the convergence of operators to some function.

math.CA↗