On (Λ, γ,)-contractions and applications to nonlinear matrix equations

Abstract

In this paper, we study the behavior of (Λ, γ,)-contraction mappings under the effect of comparison functions and an arbitrary binary relation. We establish related common fixed point theorems. We explain the significance of our main theorem through examples and an application to a solution for the following nonlinear matrix equations: X = D + Σni=1 A*i XAi - Σni=1 B*i XBi X = D + Σni=1 A*i γ (X) Ai, where D is an Hermitian positive definite matrix, Ai, Bi are arbitrary p × p matrices and γ: H(p) → P(p) is an order preserving continuous map such that γ(0) = 0. A numerical example is also presented to illustrate the theoretical findings.