Deepmala --

PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur · Department of Natural Sciences

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompass...

In this article, some new sufficient conditions for the unique solvability of a new class of Sylvester-like absolute value matrix equation \(AXB - \vert CXD \vert =F\) are given. This work is distinct from the published work by Li [Journal of Optimization Theory and Application, 195(2), 2022]. Some new conditions were also obtained, which were not...

In this note, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195-200, 2018).

This paper investigates the conditions that guarantee unique solvability and unsolvability for the generalized absolute value equations (GAVE) given by $Ax - B \vert x \vert = b$. Further, these conditions are also valid to determine the unique solution of the generalized absolute value matrix equations (GAVME) $AX - B \vert X \vert =F$. Finally, c...

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompass...

In this article we establish error bound for linear complementarity problem with P-matrix using plus function. We define a fundamental quantity connected to a P-matrix and demonstrate a method to determine bounds on the error for the linear complementarity issue of the P-type. For the quantity introduced, we find upper and lower bounds.KeywordsLine...

In this article, we present a general form of the fixed point method for processing the large and sparse linear complementarity problem, as well as a general condition for the method's convergence when the system matrix is a \(P\)-matrix and some sufficient conditions for the proposed method when the system matrix is a \(H_+\)-matrix or symmetric p...

This article presents a class of new relaxation modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). Using two positive diagonal matrices, we formulate a fixed-point equation and prove that it is equivalent to ICP. Also, we provide sufficient convergence conditions for the proposed methods when the...

In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system matrix is an $H_+$-matrix. We show the efficiency of the proposed method by using two numerical examples for diffe...

In this paper, we discussed the unique solvability of the two absolute value matrix equations. The unique solvability condition $\rho (\vert A^{-1} B \vert)<1$ is provided for the generalized absolute value matrix equation (GAVME) $AX + B \vert X \vert = F$. This condition is superior to that of Kumar et al. [J. Numer. Anal. Approx. Theory, 51(1) (...

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence analysis. Also, we demonstrate the effectiveness of our proposed method and reduce the number of iterations and CPU ti...

For solving the horizontal linear complementarity problem, we propose two projected fixed-point matrix splitting methods. The first method is based on matrix splitting, while the second method is based on the Gauss–Seidel method. We provide some convergence conditions when the system matrices are \(H_+\)-matrices. The efficiency of the proposed met...

This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is equivalent to an ICP and based on a fixed-point equation, an iterative method is presented to solve the ICP. We pr...

The singular value condition \(\sigma _\mathrm{max}(A^{-1}B)<1\) for the unique solvability of generalized absolute value matrix equation (GAVME) \(AX + B \vert X \vert = D\) is provided. Our condition is superior to the earlier published conditions \(\sigma _\mathrm{max}(\vert B \vert )\) < \(\sigma _\mathrm{min}(A)\) [1] and \(\sigma _\mathrm{max...

In this article, we take the piecewise linear equation system x − W |x| = b, which is also known as the absolute value equation, where W ∈ R^n×n, b ∈ R^n are given and to determine the value of x ∈ R^n. The absolute value equation (AVE) has many applications in various fields of mathematics like bi-matrix games, linear interval systems, linear comp...

In this article, we investigate the solution of a new class of the absolute value equation (NCAVE) A1x − |B1x − c| = d. Based on the spectral radius condition, singular value condition and row and column W-property, some necessary and sufficient conditions for unique solvability for NCAVE are gained. Some new results for the unique solvability of t...

In this article, we take the piecewise linear equation system \(x-W|x|=b\), which is also known by absolute value equation, where \(W\in {\mathbb R}^ {n\times n}\), \(b\in {\mathbb R}^{n}\) are given and to undetermined the value of \(x\in {\mathbb R}^{n}\). The absolute value equation (AVE) has many applications in various fields of mathematics li...

In this article, we present the spectral radius condition ρ(|A^(−1)| · |B|)< 1 for the unique solvability of the generalized absolute value matrix equation (GAVME) AX + B|X| = D. For some instances, our condition is superior to the earlier published singular values conditions σ_max(|B|) < σ_min(A) and σ_max(B) < σ_min(A). For the validity of our co...

A novel optimization algorithm called hybrid salp swarm algorithm with teaching-learning based optimization (HSSATLBO) is proposed in this paper to solve reliability redundancy allocation problems (RRAP) with nonlinear resource constraints. Salp swarm algorithm (SSA) is one of the newest meta-heuristic algorithms which mimic the swarming behaviour...

Keywords: Fixed point theorem Banach algebra Functional integral equation(FIE) Measure of non-compactness(MNC) Modified homotopy perturbation (MHP) a b s t r a c t In this article, we prove the existence of solution for some non-linear functional integral equations of two variables in Banach algebra C([0 , b][0 , c] , R) , b, c > 0 , which is the g...

In this article, we investigate the existence of solutions for Hadamard type two dimensional fractional functional integral equations on [1,b]×[1,c]. We use the concept of measure of non-compactness and Darbo’s fixed point theorem as the main tool to prove our results. Also, with the help of an example, we discuss the validity of our result.

In the present article, we introduce a generalization of Sz´asz-type operators which preserves test functions e0 and e2 (ei = t i, i = 0, 2). By these sequence of positive linear operators, we give better error estimation analytically using modulus of continuity. Moreover, we have shown the better approximation graphically. Further, weighted Korovk...

We study the solvability of integral equations using Darbo's fixed point theorem in Banach algebra. We prove the existence of the solution for nonlinear functional integral equations, which contain various functional integral equations in the nonlinear analysis. A numerical example showing the specified existence of our main results.

Existence of solution for functional integral equations of two variables is established in this article under some weaker conditions in a Banach algebra space \(C([0, b]\times [0, b],\mathbb {R}), b>0\) in the form of two operators. We applied the concept of measure of non-compactness (in short, MNC) and Petryshyn fixed point theorem for the operat...

In this article, we establish the existence of solution for some functional integral equations by Petryshyn's fixed point theorem in Banach algebra. Our existence results cover several existence results obtained by numerous authors under some weaker conditions. We also give some examples of functional integral equations to verify the application of...

We introduce an extension of Darbo's fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59-73, 2014). We give an example to show the specified...

We introduce sliding window rough $I-$ core and study some basic properties of Bernstein polynomials of rough $I-$ convergent of triple sequence spaces and also study the set of all Bernstein polynomials of sliding window of rough $I-$ limits of a triple sequence spaces and relation between analytic ness and Bernstein polynomials of sliding window...

In this paper we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP($q,A$) given that $A$ is real square matrix and $q$ is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context we consider the class of weak gen...

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices to these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the problem where cost component is replaced by a convex function....

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the general problem where cost component is replaced by a convex fu...

The class of functions is known as invex function (invariant convex) in the literature and the name derives from the fact that the convex like property of such functions remains invariant under all diffeomorphisms of Rⁿ into Rⁿ. A noteworthy result here is that the class of invex functions is precisely the class of differentiable functions whose st...

In this paper, we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(q, A) given that A is real square matrix and q is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context, we consider the class of generalized...

In this article, for a differentiable function $H:R^n \times R^n \rightarrow R$, we introduce the definition of the higher-order $(V,\alpha,\beta,\rho,d)$-invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations ha...

In this paper, we consider a class of generalized system of functional equations which arise in multistage decision process. We show that the coincidence solutions for this system of functional equations exist. The results presented here unify the results due to several authors. A numerical example is illustrated to justify the results.

In this paper, we discuss convergence of the \(q-\)derivatives of a new sequence of positive linear operators. We also find degree of approximation in terms of modulus of smoothness of the \(q-\)derivatives of the corresponding functions.

The aim of this article is to introduce the Kantorovich form of generalized Szasz-type operators involving Charlier polynomials with certain parameters. In this paper we discussed the rate of convergence better error estimates and Korovkin-type theorem in polynomial weighted space. Further, we investigate the local approximation results with the he...

In this paper, we study a natural modification of Sz\'{a}sz - Mirakjan operators. It is shown by discussing many important established results for Sz\'{a}sz - 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 mea...

In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of continuity, Peeters K-functional, weighted modulus of continuity and Lipschitz class are considered to prove our resu...

In this article we introduce the sequence spaces \\$\left[\chi^{2q}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\rig...

In this paper the iterates of the \(q\)-Durrmeyer operators are introduced using a modification. For these iterates the convergence results are obtained. The estimates for the rate of convergence are obtained in terms of the modulus of smoothness. A Voronovskaya type asymptotic result is obtained. Finally necessary conditions are derived which guar...

This paper deals with the existence, uniqueness and iterative ap- proximations of solutions for the functional equations and system of functional equations arising in dynamic programming of multistage de- cision making processes in Banach spaces and complete metric space, respectively. The results presented in this paper unify and generalize many k...

In this paper, we study the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming under Banach spaces and complete metric spaces. Our results unify the results of Bellman [1], Bhakta and Mitra [3], Bhakta and Choudhury [4], Liu [8], Liu and Ume [10], Liu et al. [11], Liu et al....

In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some addition...

In the present paper, a new theorem on the degree of approximation of function f∼, conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz W(Lr,ξ(t))(r⩾1)W(Lr,ξ(t))(r⩾1)-class by dropping the monotonicity condition on the generating sequence {pn} has been established which in turn generalizes the results of Lal (2009)...

The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces BC(S) and B(S) and complete metric space BB(S), respectively. Our main results extend, improve, and generalize the results due to several autho...

In the present paper, we study an inverse result in simultaneous approximation for Baskakov-Durrmeyer-Stancu type operators. MSC: 41A25, 41A35, 41A36.

In this paper, we prove the existence of solutions of some nonlinear functional-integral equation by using a fixed point theorem which satisfy the Darbo condition. The results extend the corresponding results of many authors. In the sequel, we give an example of our main result to highlight the realized improvements.

In this paper, using the technique of measure of noncompactness in Banach algebra, we prove an existence theorem for a nonlinear integral equation which contains as particular cases a lot of integral and functional-integral equations considered in nonlinear analysis and its applications. Our claim is also illustrated with the applications to some n...

In this paper, we define PDPD-operator pair of single valued mappings and obtain some common fixed point theorems for this class of maps under relaxed conditions. Our theorem generalizes results of Bhatt et al. [A. Bhatt, H. Chandra, D.R. Sahu, Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonline...

In this paper, we define PP-Lipschitzian maps and focus our attention on some fixed point theorems of Dhage on a Banach algebra. It is shown that these results can be proved under weaker conditions. Our claim is also illustrated with some examples.

In this paper, we study solvability of two functional equations arising in dynamic programming of multistage decision processes. By using Boyd and Wong fixed point theorem, some existence and uniqueness theorems of solutions and iterative approximation for solving these class of functional equations are established. The results presented here exten...

We establish a fixed point theorem for two pair of maps satisfying a contractive type condition by using the concept of occasionally weakly compatible maps. As application, the existence and uniqueness of common solutions for certain systems of functional equations arising in dynamic programming are discussed by using the common fixed point theorem...