Modified semi-linear uniform spaces and new types of contractions

Abstract

In 2009 Tallafha, A. and Khalil, R. defined a new type of uniform space namely, semi-linear uniform space [8]. Later Tallafha, A. in [9], [10] and [11], Alhihi, S. in [1] and Tallafha, A. and Alhihi, S. in [12], gave more properties of semi-linear uniform spaces. Also Lipschitz condition and contraction mapping on semi-linear uniform spaces are defined, which enables one to study fixed point for such functions.

In this article we shall define a modified semi-linear uniform space and a new type of contractions on semilinear uniform spaces, finally we ask the following natural question. If f is a contraction from a complete modified semi-linear uniform space (X,Γ) to itself, is f has a unique fixed point.