Solving systems of nonlinear matrix equations involving Lipshitzian mappings

Abstract

In this study, both theoretical results and numerical methods are derived for solving different classes of systems of nonlinear matrix equations involving Lipshitzian mappings. 2000 Mathematics Subject Classifications: 15A24; 65H05.

Iterative approximation of fixed points of generalized weak Presic type k-step iterative method for a class of operators

“…Let (X, d) be a complete metric space, k a positive integer and f : X k → X be a given mapping. Suppose that there exists λ ∈ [0, 1) such that 5) for all (x 1 , . .…”

“…In the last few years there has been a constantly increasing interest in developing the theory and numerical approaches for positive definite solutions to the nonlinear matrix equation of the form (3.7) (see, for example, [5,9,14]). …”

Solving a class of nonlinear matrix equations via the coupled fixed point theorem

“…The set HðnÞ endowed with this norm is a complete metric space. See [14,11,1] for more details. In [1], Ran and Reurings considered two classes of matrix equations:…”

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

“…The set H.n/ endowed with this norm is a complete metric space. See [28][29][30] for more details. Moreover, we see that H.n/ is a partially ordered set with partial order which is defined by X Y " Y X:…”