Vishnu Narayan Mishra

Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, 484 887, Madhya Pradesh, India · Mathematics

The motive of this research article is to introduce a sequence of Szász 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 approxim...

In this study, we construct a new sequence of bivariate Summation-integral type hybrid operators and their approximation behavior. Moreover, the rate of convergence of these operators is given by using the modulus of continuity. Further, Lipschitz-maximal, Peetre’s K-functional and global approximation results are investigated using weight function...

A rational function can always be integrated, that is, the integral of such a function is always an elementary function. The integration procedure is complex and consists of four steps: elimination of the common zero-points of the numerator and denominator, reduction to a true rational function, decomposition into partial fractions and integration...

In this paper, we have considered a non-linear mathematical model to study the chaotic situation, arising due to slow process of recruitment, leading to an increase in unemployment. We observed the effects on recruitment process due to delay and without delay. We have also studied the stability of equilibrium points with numerical examples to compa...

In this paper, fitted operator finite difference methods are presented for two-parameter singularly perturbed one-dimensional parabolic partial differential equations with a delay in the time variable. Such boundary value problems are frequently encountered in the spatial diffusion of reactants and in control systems. To approximate the solution of...

This paper presents a Stancu-type generalization of Szasz operators linked to Hermite polynomials. The convergence properties of these operators are discussed by utilizing Korovkin’s theorem. Additionally, the paper explores approximation theorems for these operators using various tools, including Peetre’s K-functional, classical and second-order m...

This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of T-norm and S-conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature on Pythagorean and FFSG, the standard properties for me...

Data envelopment analysis (DEA) is a non-parametric approach for the estimation of production frontier that is used to calculate the performance of a group of similar decision-making units (DMUs) which employ comparable inputs to produce related outputs. However, observed values might occasionally be confusing, imprecise, ambiguous, inadequate, and...

In this chapter, a pair of nondifferentiable multiobjective symmetric fractional duality models with cone function are formulated in a vector optimization problem, where each component of the objective function contains support function of a compact convex set. The K-\((C, \rho )\)-convexity and K-\((C, \rho )\)-quasiconvexity functions are defined...

Multiprogramming plays an essential role more effectively in resources utilization. In the context of multiprogramming, CPU scheduling plays a key role. Several algorithms have already been introduced to achieve the objectives of CPU scheduling. Among these, Round Robin is one of the important CPU scheduling algorithms, but time quantum and unneces...

In this paper, under some conditions in the Banach space $ C ([0, \beta], \mathbb{R}) $, we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder a...

Inventory control is considered one of the most widely documented topics in the reality. Fractional derivatives and integration is the part of fractional calculus. Fractional calculus is the generalized part of ordinary calculus. The memory of physical phenomena is a highly concerning topic but it is neglected with describing in terms of integer-or...

In this paper, utilizing the technique of generalized Darbo's fixed‐point theorem associated with measure of noncompactness in Banach space, we analyze the existence of solution for a class of nonlinear functional integral equations involving Erdélyi–Kober fractional operator. The existing result was obtained to strengthen the ones mentioned previo...

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 Fa\`{a} di Bruno's for...

In this paper, we have established a very interesting result for the degree of approximation of conjugate functions belonging to the $W[L_{r},\xi(t)]$ class by generalized N\"{o}rlund-Euler product summability method of conjugate series of Fourier series. The results presented in this paper is the generalization of many known and unknown results.

This paper proposes a simple idea to speed-up the convergence of a fixed-point iteration for Fredholm equation defined on a mesh. First, the analytical problem is discretized by using quadrature rule and col-locating at mesh points. Banach Fixed-Point Theorem is used to construct a discrete Picard scheme (PS). To accelerate the computations, the Pi...

In the present paper, we introduce a modification of Sz\'asz operators involving generalized Brenke type polynomials. First, we investigate Korovkin's type approximation theorem. Next, we established an approximation result for the functions in Lipschitz type space. Furthermore, we discuss the rate of convergence by means of the Ditzian-Totik modul...

In this paper, we introduce a modified Bernstein-type operators based on two real parameters and study its various approximation properties. We derive some direct results e.g. Voronovkaja type asymptotic theorem, an estimate of error in ordinary as well as in Ditzian Totik modulus of smoothness and an error estimate for functions belonging to the L...

n any business memory effect has great importance in inventory management as memory or past history cannot be ignored from the practical life of the inventory system. Many exogenous inventory parameters and factors at a given time depends not only their current values but also on the past histories. Thus an inventory management is a non Markovian p...

In this article, we prove a new compactness criterion in the Lebesgue spaces $L_p({\mathbb{R}}^+), 1 \leq p < \infty$ and use such criteria to construct a measure of noncompactness in the mentioned spaces. The conjunction of that measure with the Hausdroff measure of noncompactness is proved on sets that are compact in finite measure. We apply such...

In the present research work, we have derived two theorems which involves integral operators of Erdélyi-Kober type and a q-analogue of modified multivariable I-function. The related averment for the Riemann-Liouville and Weyl fractional basic integral transforms are also deduced. A number of corollaries concerning the basic analogue of modified mul...

The key goal of the present research article is to introduce a new sequence of linear positive operator i.e., α-Schurer Durrmeyer operator and their approximation behaviour on the basis of function η(z), where η infinitely differentiable on [0, 1], η(z) = 0, η(1) = 1 and η (z) > 0, for all z ∈ [0, 1]. Further, we calculate central moments and basic...

This work emphasis on the basic notions regarding the Neutrosophic Fuzzy Sets (NFSs) with operations and their applicability in medical diagnostic process. In this manuscript, we developed neutrosophic fuzzy set-based Monte Carlo simulation technique for the decision making in medical diagnostic processin fuzzy environment. In this work, we managed...

In this research paper, the authors studied some problems related to harmonic summability of double Fourier series on Nörlund summability method. These results constitute substantial extension and generalization of related work of Moricz [ 1 ] and Rhodes et al. , [ 2 ]. We also constructed a new result on \((N,p^{(1)}_b,p^{(2)}_a)\) by regular Nörl...

In this paper, we define θ-expansions on Branciari metric spaces by complementing the concept of θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014). Also, we present some new fixed point results for θ-expansion mappings on a Branciari metric space.

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.

This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (κ,ϕ)-Riemann–Liouville along with Erdélyi–Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theor...

The aim of this chapter is to construct the new sequence of Szász-type operators involving q-Appell polynomials and study some basic properties for the new operators. We also investigate the local approximation results via Peetre’s K-functional, Lipschitz class and modulus of smoothness. Moreover, we discuss the weighted approximation results and s...

In this paper we introduce new bivariate Bernstein type operators BnM,i(f; x, y), i = 1, 2, 3. The rates of approximation by these operators are calculated and it is shown that the errors are significantly smaller than those of ordinary bivariate Bernstein operators for sufficiently smooth functions.

This paper deals with the approximation properties of the summation-integral type operators defined by Mishra et al. (Boll Unione Mat Ital 8:297–305, 2016). It consists of the local results and convergence theorem of the defined operators. Here, we discuss the asymptotic behaviour of the operators and the quantitative means of Voronovskaja type the...

In this article, an inventory model has been developed by incorporating the effect of the past experience. This paper wants to incorporate memory effects that are based on the fact that economic agents remember the history of changes in exogenous and endogenous variables. Memory or past experiences have a great impact on the real inventory system t...

In this research paper, we developed a new method to investigate the posfust reliability of a substation automated system. Failure rates and repair rates of the system are key elements of an automated system. In our method, we considered the fuzzy failure and fuzzy repair rates in the context of possibility. In this approach, a decomposition method...

In this paper, the Durrmeyer-type modification of Szász-type operators using the Beta function is introduced. First, some fundamental properties of these operators are studied and then approximation properties of a sequence of these operators using the Korovkin theorem are investigated. The rate of approximation by the modulus of continuity is esti...

The paper is devoted to the study of a Pal type (0;1) interpolation problem on the unit circle considering two disjoint sets of nodes. The nodal points are obtained by projecting vertically the zeros of the Jacobi polynomial P _n^{(α,β)}(x) and its derivative P _n^{(α,β)'}(x) , together with ±1 onto the unit circle. The Lagrange data are prescribed...

Special functions rely heavily on hypergeometric functions. Recently, researchers introduced the (p, k) analogue of the hypergeometric function and its different properties. The Lauricella functions are the generalization of the Gauss hypergeometric function in the n-variables. In this manuscript, we introduced (p1, p2, ⋯ , pn, k) analogue of Lauri...

We relate this article to the emerging idea of distinguishability of conformable linear hybrid time-invariant control systems. To obtain the necessary and sufficient conditions of α \alpha -distinguishability for fractional cases, we develop the Leibnitz rule for conformable derivatives. Furthermore, with the help of a study of Laplace techniques,...

In this study, Data Envelopment Analysis (DEA) models are improved by employing spherical fuzzy sets (SFSs), which is an extension of generalized fuzzy sets. SFSs were recently introduced as a novel type of fuzzy set that allows decision-makers to express their level of uncertainty directly. As a result, SFSs provide a more preferred domain for dec...

Teachers are increasingly required to have mathematical subject knowledge described as lists of facts, skills and competencies. Different emotional reactions are present in the classroom every day. Emotional reactions are most often divided into positive and negative, and negative emotional reactions are most often related to the evaluation process...

This article evaluated the agricultural performance of 31 states and union territories (UTs) in India from 2012 to 2017. The best agricultural productivity states and UTs in India were obtained using Malmquist based DEA technique and the efficiency s core f or e ach y ear w as found using CCR model. The input parameter is taken as annual rainfall,...

The fractal geometries are applied extensively in many applications like pattern recognition, texture analysis and segmentation. The application of fractal geometry requires estimation of the fractal features. The fractal dimension and fractal length are found effective to analyze and measure image features, such as texture, resolution, etc. This p...

In this paper, we define the concepts of ϕ-contraction and point-wise Φ-contraction in modular metric space. Next we give some conditions that guarantee the existence and uniqueness of fixed points of self-mappings in modular metric spaces. Finally we give an application to Caratheodory’s type anti-periodic boundary value problem.

It is well-known to everyone that the system is very much disturbed for the past experience effect. Past experiences should be incorporated to the system. For rapidly changing market, cost parameters of the inventory system are highly uncertain. Due to the above reasons, in this paper, our intention is to develop an EOQ model with constant demand r...

This work is the first to investigate the Data Envelopment Model (DEA) in the presence of q-Rung fuzzy inputs and outputs. Fundamental CCR and BCC models are presented in the context of q-Rung triangular fuzzy numbers (qRTFNs), which take into account the truth and falsity membership degrees of each input and output and provide a novel solution app...

In this paper, we introduce the idea of -expansion by employing tri-simulation functions introduced by Gubran et al. [R. Gubran, W. M. Alfaqih and M. Imdad, Italian Journal of Pure and Applied Mathematics -N, 45 (2021) 419-430] in a metric space. Further, we shall use these mappings to study various fixed point results in complete metric spaces. Th...

The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(\cdot )-f\left(\cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the r th differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are c...

Generally, linear programming (LP) problem is the most extensively utilized technique for solving and optimizing real-world problems due to its simplicity and efficiency. However, to deal with the inaccurate data, the neutrosophic set theory comes into play, which creates a simulation of the human decision-making process by considering all parts of...

This paper presents innovative series and summations derived from the optimized combinations relating to the combinatorics. These series and summations will be useful for the researchers who are involving to solve the scientific problems.

The concept of fuzzy set, intuitionistic set, and mediative fuzzy set as a generalization of a crisp set have been introduced in many real-life applications. The concept of crisp relation between elements of sets can be extended to fuzzy relations. Extended relations will be considered as relations on fuzzy sets. In this work, we developed the conc...

In this paper, we define a generalized resolvent operator involving a 𝒢 ⁢ ( ⋅ , ⋅ ) -co-monotone mapping for solving a generalized variational inclusion problem. We show that the resolvent operator under consideration is single-valued as well as Lipschitz continuous. An iterative algorithm is constructed to obtain the approximate solution of our pr...

The paper is devoted to the study of a Pál type (0; 1) interpolation problem on the unit circle considering two disjoint sets of nodes. The nodal points are obtained by projecting vertically the zeros of the Jacobi polynomial P_n^(α, β)(x) and its derivative P_n^(α, β)' (x), together with ±1 onto the unit circle. The Lagrange data are prescribed on...

Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled K-frame or controlled operator frame in Hilbert C *-modules. We establish the equivalent condition for controlled K-frame. We...

The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fejér inter-polatory conditions on the zeros of Chebyshev Markov sine fraction on [−1, 1).

The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Szász-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, ra-pidity of convergence and order of approximation are...

The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz´asz-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, rapidity of convergence and order of approximation are...

In the present analysis, Boundary layer flow over a moving plate in a nanofluid with Viscous Dissipation in saturated porous medium is analyzed. Using proper similarity transformations, the governing nonlinear PDEs were transformed into a system of nonlinear ODEs. Governing boundary value problem is numerically solved using 4th order Runge-Kutta sh...

The Wiener index of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text] where the sum is taken through all unordered pairs of vertices of [Formula: see text] and [Formula: see text] is distance between two vertices [Formula: see text] and [Formula: see text] of [Formula: see text]. Let [Formula: see text]...

In an uncertain situation, data may present in continuous form or discrete form. We have various techniques to deal with continuous data in a realistic situation. However, when data are in discrete form, the existing techniques are inadequate to deal with these situations, and these techniques cannot provide the proper modulation for adequate analy...

In this paper, we introduce a two parameter generalization of Lupas-Kantorovich operators based on Polya distribution. We obtain the moments of the operators by deriving a recurrence relation and then prove and study Voronovskaja-type asymptotic theorem, local approximation, weighted approximation, rate of convergence and pointwise estimates using...

The goal of the present manuscript is to introduce a new sequence of linear positive operators, i.e., Sz´asz-Schurer-Beta type operators to approximate a class of Lebesgue integrable functions. Moreover, we calculate basic estimates and central moments for these sequences of operators. Further, rapidity of convergence and order of approximation are...

Soft computing approaches have been used for confronting the fuzzy embedded process in various decision-making problems. Traditional fuzzy sets (FS), intuitionistic fuzzy sets (IFSs), and Pythagorean fuzzy sets (PFS) frequently applied in the measurement of correlation coefficient techniques based on similarity and distance for various parameters....

This paper deals with the approximation properties of a generalized version of Szász–Mirakjan operators which preserve a x {a^{x}} , a > 1 {a>1} (fixed), and x ≥ 0 {x\geq 0} . The uniform convergence of the operators is studied by using some auxiliary results. Also, error estimations are determined by considering the functions from different spaces...

This paper deals with Hadamard inequalities for strongly m-convex functions via Riemann-Liouville fractional integrals. These inequalities provide refinements of well known fractional integral inequalities for convex functions. Further, by applying an identity error estimations are obtained and compared with already known error estimations.

This work is of multidisciplinary concept, whose development is difficult to perform. Considering also that, in one of the steps, the similarity between the FRF of the vibration and acoustic signal is demonstrated. The objective of this work is the analysis and prognosis of the progression of failures of a pair of gears using the artificial immune...

We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces(IFNS), and obtain necessary and sufficient Tauberian conditions under which convergence of double sequences in IFNS follows from their weighted mean summability. This study reveals also Tauberian results for some known summation methods in the speci...

Generally, linear programming (LP) problem is the most extensively utilized technique for solving and optimizing real-world problems due to its simplicity and efficiency. However, to deal with the inaccurate data, the neutrosophic set theory comes into play, which creates a simulation of the human decision-making process by considering all parts of...

In this study, stability analysis of an unhealthy diet model involving immune cells and abnormal cells with antiangiogenesis treatment is discussed. We determined the feasibility of the solution, the conditions for the local stability of all equilibrium points by using standard stability analysis and including global stability condition for the tum...

Our main aim is to investigate the approximation properties of 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 the weight function, the weighted statistical convergence theorem with t...