Fixed Points of Set-valued F-contraction Operators in Quasi-ordered Metric Spaces with an Application to Integral Equations

Abstract

In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since we present Banach contraction principle in a different manner from that which is known in the present literature. Some examples and an application to existence of solution of Volterra-type integral equation are given to support the obtained results