A vector version of the fixed point theorem of cone compression and expansion for a sum of two operators

Lyna Benzenati; Karima Mebarki; Radu Precup

Lyna Benzenati Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, 06000 Bejaia, Algeria
Karima Mebarki Bejaia University
Radu Precup Departement of Mathematics, Babe\c{s}--Bolyai University, 400084 Cluj-Napoca, Romania

Abstract

In this work, we establish a vector version of fixed point theorem of cone compression and expansion for an expansive operator with constant h>1 perturbed by a k-set contraction when 0\leq k<h-1. We give the compression-expansion conditions on components to allow the nonlinear term of a system to have different behaviors both in components and in variables. An example is given to illustrate our theoretical result.