Common Positive Solution of Two Nonlinear Matrix Equations Using Fixed Point Results

Abstract

We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1kBi*G(X)Bi, where R1,R2∈P(n), Ai,Bi∈M(n), i=1,⋯,k, and the operators F,G:P(n)→P(n) are continuous in the trace norm. We go through the necessary criteria for a common positive definite solution of the given NME to exist. We develop the concept of a joint Suzuki-implicit type pair of mappings to meet the requirement and achieve certain existence findings under weaker assumptions. Some concrete instances are provided to show the validity of our findings. An example is provided that contains a randomly generated matrix as well as convergence and error analysis. Furthermore, we offer graphical representations of average CPU time analysis for various initializations.

Common fixed point Theorems for Interpolative Mapping in Bicomplex-valued b-Metric Space with An application to Non-linear matrix Equation

“…The motivation of this manuscript is to prove the common fixed point theorem for interpolative contraction mappings in bicomplex valued b-metric space. In particular, we generalize and extend the results proved by Beg et al [5], Mani et al [17], Datta et al [7], Nashine et al [20] and Joseph et al [12].…”

“…Recently, the study of nonlinear matrix equations was given by Garai and Dey [9] gave a common solution to a pair of non-linear matrix equations via fixed point results. Nashine et al [20] proved a common positive solution of two nonlinear matrix equations using fixed point Results. Joseph et al [12] gave the results by solving a system of linear equations via bicomplex valued metric space.…”

Common fixed point theorems for interpolative mappings in bicomplex-valued b-metric spaces with an application to non-linear matrix equations

“…This manuscript aims to prove some common fixed point theorems for interpolative contraction mappings in bicomplex valued b-metric spaces. In particular, we generalize and extend the results proved by Beg et al [5], Mani et al [23], Datta et al [9], Nashine et al [26] and Joseph et al [14].…”

“…Recently, the study of nonlinear matrix equations was given by Garai and Dey [11] who gave a common solution to a pair of non-linear matrix equations via fixed point results. Nashine et al [26] found a common positive solution of two nonlinear matrix equations using fixed point Results. Joseph et al [14] gave some results by solving a system of linear equations via a bicomplex valued metric.…”

On a Unique Solution of the Stochastic Functional Equation Arising in Gambling Theory and Human Learning Process

“…It has been extended and generalized in numerous directions (for the detail, see [16][17][18]). We suggest the reader to see [19][20][21] for further information on fixed point theory and its applications in various spaces.…”