Fixed point theorems for generalized semi-quasi contractions

Abstract

In this note, we introduce the notion of a generalized semi-quasi contraction and obtain a fixed point theorem for such contraction. Our results extend and generalize some well-known fixed point theorems including Ciric’s quasi contraction theorem. As an application of our main theorem the existence of a solution for a class of functional equations arising in dynamic programming is discussed. At the end an open problem is also posed.