Abstract
The aim of this paper is to establish certain new fixed point results for multi-valued as well as single-valued maps satisfying an alpha-psi-contractive conditions in complete metric space. As an application, we derive some new fixed point theorems for psi-graphic contractions defined on a metric space endowed with a graph as well as an ordered metric space. The presented results complement and extend some very recent results proved by Asl et al. (Fixed Point Theory Appl. 2012: 212, 2012) and Samet et al. (Nonlinear Anal. 75: 2154-2165, 2012) as well as other theorems given by Hussain et al. (Fixed Point Theory Appl. 2013: 212, 2013). Some comparative examples are constructed which illustrate the superiority of our results to the existing ones in the literature.