Vishnu Narayan Mishra

• Ph.D. from Indian Institute of Technology, Roorkee, Uttarakhand, India in July 2007.
• Professor at Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, 484 887, Madhya Pradesh, India

The paper aims to introduce the notion of F-metric spaces and establish α-fixed point results for fuzzy enriched ϕ − ψ contraction in complete F-metric spaces. These contributions extend the existing literature on fuzzy mappings and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed results. A...

Direct solution of Higher of ordinary differential equations have yet to gain more attention and be explored extensively despite it’s vast presence in sciences and engineering. This study employs hybrid block methods within a step interval with higher order and good precision to directly solve third-order problems of ordinary differential equations...

In this chapter, we explore the historical development of the significant results surrounding λ-Bernstein operators within the field of approximation theory. The primary objective of this study is to review the progress in this area and evaluate both the rapidity of convergence, using the modulus of continuity, and the rate of convergence, utilizin...

In this paper, we present some fixed point results in the setting of quasi-metric spaces by using the concept of α-admissible mappings to prove Eldeisten-Suzuki-type contraction. Additionally, we apply our main results to establish a bounded solution of a functional equation arising in dynamic programming, and we provide illustrative examples to de...

The paper aims to introduce the notion of L-fuzzy mapping and establish-fuzzy fixed point results for rational contraction in a complete-metric spaces. These contributions extend the existing literature on fuzzy mappings and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed results. Also, we...

Here, we will investigate at isotropic and flat FRW universe which contains pressure less cold dark matter (CDM) with Tsallis holographic dark energy (THDE). For getting the exact solutions to the Einstein field equation, we use the hybrid expansion law (HEL), which is a result of merging the power and exponential laws. The physical as well as geom...

In this study, Genetic Algorithm (GA), a sort of randomized direct, iterative search methodology built around natural selection, is employ in computers to discover approximations of solutions to optimisation and search issues. GA employs operators including selection, crossover, and mutation to tackle. In case of NP-hard issues, particularly for tr...

The main aim of this article is to design a novel framework to study a generalized fractional integral operator that unifies two existing fractional integral operators. To ensure the suitable selection of the operator and with the discussion of special cases, it is shown that our considered fractional integral generalizes the well-known Atangana–Ba...

This paper aims to prove some coincidence point results for three single-valued mappings in the setting of metric spaces and partially ordered metrics spaces satisfying a generalized contraction condition of rational type. These contributions extend the existing literature on three single-valued mappings and fixed point theory. We showcase the prac...

In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a binary relation. We accomplish this by generalizing several key notions from metric fixed point theory, such as completeness, closedness, continuity, g-continuity, and compatibility, to the relation-theoretic setting. We then use these gen...

The present work involves the study of ferrofluid flow over a stretchable rotating disk maintained at an uniform temperature in the presence of magnetic field dependent viscosity. The system is analyzed through the Jenkins model and the simplified governing equations are represented in the cylindrical co-ordinates. The obtained nonlinear coupled pa...

The paper aims to introduce some fixed point results in the setting of sequential compact b-metric spaces to prove Eldeisten-Suzuki-type contraction for self-mappings. These contributions extend the existing literature on fixed point for ordered metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicabi...

The paper aims to introduce novel concepts of fuzzy type contractions and establish fixed point theorems for fuzzy mappings within the framework of fuzzy cone metric spaces. These contributions extend the existing literature on fuzzy mappings and fixed point theory. Through illustrative examples, we showcase the practical applicability of our propo...

Purpose This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, i...

It is well-known to everyone that the system is very much disturbed by the past experience effect so past experiences should be incorporated into the system. For a rapidly changing market, the cost parameters of the inven tory system are highly uncertain. Due to the above reasons, in this paper, we want to develop an EOQ model with a constant deman...

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partia...

In this article, we build a pair non-differentiable second-order symmetric multiobjective fractional variational programming models with cone constraints, where each objective function component has a support function for a compact convex set. The ( C, ρ, θ )-convexity/( C, ρ, θ )-pseudo-convexity/( C, ρ, θ )-quasiconvexity functions are defined an...

This article is involved with the solvability to fractional integral equations concerning Riemann-Liouville on a Banach space C([0, b]) arising in some engraining problem. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the measure of non-compactness(MNC). To find this purpose, we utilize...

The aim of this paper is to established some fixed point results in complete hyperbolic spaces and convergence of M iteration scheme for nearly asymptotically nonexpansive mappings. Our results generalizes the results given by Sharma from CAT(k) spaces to complete hyperbolic spaces.

The goal of this manuscript is to introduce a new sequence of generalized-Baskakov-Durrmeyer-Schurer Operators. Further, basic estimates are calculated. In the subsection sequence , rapidity of convergence and order of approximation are studied in terms of first and second order modulus of continuity. We prove a Korovkin-type approximation theorem...

Solving systems of nonlinear equations (NESs) is a significant and challenging task in the field of sciences and engineering. This article proposes a modified differential evolution (MDE) to solve the NESs problem. Using principle of the particle swarm optimization, it employed novel mutation structure with modernistic control factors, to heighten...

The purpose of this study is to look at the changes that computers have made in mathematics itself and in the mathematics curriculum. The aim of the study is to investigate the various applications of computers in education in general, especially in mathematics education, and their application in the mathematics curriculum and in the teaching and l...

This paper aims to examine the expansion of periodic functions using wavelet bases. M. Skopina [8] obtained a Wavelet analog of the classical Jackson’s theorem for trigonometric approximation. Our result generalizes the result of M. Skopina [8] and V. Karanjgaokar et al. [15].

This paper deals with the approximations of the functions by generalized Durrmeyer operators of Szász–Mirakjan, which are linear positive operators. Several approximation results are presented well, and we estimate the approximation properties along with the order of approximation and the convergence theorem of the proposed operators. For an explic...

In the operation of power systems, economic dispatch (ED) plays a vibrant role. Its key aim is to find the best efficient distribution of power between generating units. Also, it converted into non-convex nature due to considering many practical restrictions like maximum and minimum power output, prohibited operating zones, transmission line capaci...

This paper provides study on King-type modification of some linear positive operators, viz., Lupaş, Szasz-Mirakjan, Baskakov operators. In the paper, density theorems for the operator and their modifications are presented and comparison on the rate of convergence between original and modified operators are mentioned. In support to the mathematical...

Runge’s phenomenon reveals that interpolation methods lack uniform convergence of the sequence of the thus constructed polynomials to the function. The linear positive operators, however, can be relied on to ensure convergence across the whole domain. Further, linear positive operators can be modified suitably to approximate integrable functions. I...

This paper deals with bivariate Stancu-type generalization of Jakimovski–Leviatan–Durrmeyer (JLD) operators in the approximation theory. Korovkin-type approximation properties of modified operators are also examined. Rate of convergence of these operators are investigated by means of the full and partial modulus of continuity. Further, weighted app...

Purpose This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized meth...

Nowadays, the differential evolution (DE) achieved noticeable progress and solved a wide range of non-linear/non-convex engineering optimization issues. As a strong optimizer, DE has many advantages like simple structure, strong exploitation ability and considerable convergence speed. However, DE also suffers from low diversification, poor explorat...

p>Amid a lot of evolutionary methods (EMs), differential evolution (DE) is broadly used for various optimization issues. Though, it has rare shortcomings such as slow convergence, stagnation etc. Likewise, mutation and its control factor choice for DE is extremely inspiring for enhanced optimization. To increase the exploration competence of DE, a...

The purpose of this article is to extend the classical Banach contraction principle to a complete metric space endowed with a binary relation where the contraction condition is relatively weaker than usual contraction as it is required to hold only on those elements which are related under the underlying relation rather than the whole space. Finall...

In this paper, we introduce and study a class of mappings called generalized-contractive mappings, which are a generalization of the well-known-contractive mappings. We explore various fixed point theorems for such mappings in complete metric spaces, using the concept of-admissible mappings. Additionally, we apply our main results to establish fixe...

In this paper, a generalization of Lupa¸s operators is defined which establishes better convergence. This generalized Lupa¸s operator satisfies the Korovkin conditions for density theorems for the extended value of parameter a, and also leads to better approximation results. This generalization removes the limitation of Lupa¸s operators which satis...

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 collocating at mesh points. Banach Fixed-Point Theorem is used to construct a discrete Picard scheme (PS). To accelerate the computations, the Pic...

The paper aims to introduce novel concepts of fuzzy type contractions and establish fixed point theorems for fuzzy mappings within the framework of fuzzy cone metric spaces. These contributions extend the existing literature on fuzzy mappings and fixed point theory. Through illustrative examples, we showcase the practical applicability of our propo...

The paper aims to introduce some fixed point results in the setting of sequential compact b-metric spaces to prove Eldeisten-Suzuki-type contraction for self-mappings. These contributions extend the existing literature on fixed point for ordered metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicabi...

In this paper, the degree of trigonometric approximation of bivariate periodic Hölder class functions have been studied using double sub-matrix means of DFS (double Fourier series). In this consequence we have obtained two new results for approximation under p f-norm and ξ p f-norm.

In this article, we establish the existence and uniqueness of fixed points for rational type contraction mappings in a metric space that is equipped with a partial order. Our results are shown to improve upon previous results in the literature, and we provide illustrative examples to demonstrate the effectiveness of our approach. Mathematics Subjec...

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems...

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...

This paper aims to describe the application of educational tools with which it can develop interactivity and help pupils and students to better and more clearly understand mathematics and to understand that it is all around us, that it is our everyday life. The paper will show the ways of creating mathematical educational materials and their use. T...

Among popular evolutionary algorithms (EAs), Differential Evolution (DE) is secondhand for comprehensive optimization. However, it has numerous restrictions like slow convergence, stagnation etc. Moreover, in DE choice of its mutation and control factor is also challenging for better optimization. To enhance search capability of DE, a modified diff...

In this article, we introduce generalized beta extension of Sz $$\acute{a}$$ a ´ sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin-type theorem and modulus of continuity for the spa...

In order to approximate Lebesgue integrable functions on [0, 1], a sequence of linear positive integral operators of Kantorovich type Lσ f (x) with a parameter sσ is introduced. The estimates for rates of approximation for functions with a specific smoothness are proved using the appropriate modulus of continuity.

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...

In the modern world, software is practically inevitable and present everywhere. Today, software represents the key to the success of most computer systems and at the same time the differentiation factor of the organizations that own it. Software has become an essential component in healthcare decision-making and the basis of scientific research and...

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...

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...

Super Metric Spaces are a ground-breaking generalization of metric spaces that were recently developed by Karapinar and Khojasteh (Filomat, in press). In this paper, we initiate the study of expansive fixed points in the context of the supermetric spaces. Our results may open the door to more expansive fixed point results in a different direction.

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...