Metric Fixed Point Theorems for Single-valued and Multi-valued Mappings

Abstract

Metric Fixed Point Theorems for Single-valued and Multi-valued Mappings The main goal of the present research is to establish existence and uniqueness theorems regarding fixed points, coincidence points and common fixed points of single-valued and multi-valued mappings in connection with contractive type inequalities in complete metric spaces and generalized metric spaces. Some notions namely generalized α*- Mizoguchi-Takahashi type contraction, generalized Mizoguchi-Takahashi G contraction and α-admissible mappings for cone metric space are also obtained. We also include an application in which we prove the existence and uniqueness of a solution for a general class of Fredholm integral equation of 2nd kind. To enhance the validity of this work some interesting examples are also furnished.