Approximate Fixed Point Results for Rational-type Contraction Mappings

Abstract

In the paper [Tijs, S., Torre, A. and Branzei, P.: Approximate fixed point theorems, Libertas Mathematica, 23(2003),35−39(2003)], the authors studied some fixed point theorems by considering weakening of the conditions in the fixed point theorems of Brouwer, Kakutani and Banach which still guarantee the existence of approximate fixed points. Also, in the paper [Berinde, M.: Approximate fixed point theorems, Studia Univ. BABES-BOLYAL, MATHEMATICA, Volume L1, Number 1, pp. 11−23(2006).], the author gave some qualitative and quantitative approximate fixed point results on metric spaces by introducing two Lemmas, and using some contactive-type operators used by Tijs etal. The aim of this paper is to establish qualitative and quantitative approximate fixed point results involving rational type contraction mappings in metric spaces (not necessarily complete). Our results are extensions of several others in the literature. Some examples are provided to illustrate our results.