In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.

Received: December 21, 2010 Accepted: January 7, 2011 doi:10.5539/jmr.v3n2p151 Abstract In this paper, we study fixed point theorems for multi-valued weak contractions. We show that the Picard projection iteration converges to a fixed point, give a rate of convergence and generalize Collage theorem. This work includes results on multi-valued contraction mappings studied by (Kunze, H.E., La Torr...

Compared with the previous work, the aim of  this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we introduce a cone generalized semi-cyclicφ−contraction maps and prove best proximity points theorems for such mapsin cone metric spaces. Also, we study existence and convergence results ofbest proximity points of such maps in normal cone metric spaces. Our resultsgeneralize some results on the topic.