Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application

Abstract

In this article, we introduce a relatively new concept of multi-valued ( θ , R ) -contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

Keywords

• fixed point
• monotone type mappings
• multi-valued <i>θ</i>-contractions
• binary relations
• integral equations