A fixed-point principle for a pair of non-commutative operators

Abstract

In this paper, a fixed point principle for a pair of operators (fi,X,d), i = 1,2, where (X,d) is a metric space and f1, f2: X → X, is established under the generalized uniform equivalence condition of different orbits generated by the maps f1 and f2 separately, which gives another generalization of the fixed point principle of Leader [1] and estimates approximations to the fixed points of both the operators simultaneously.