Fixed point theorems for singlevalued mappings and multivalued mappings in generalized metric space

Abstract

In this thesis, we prove a number of single-valued and multi valued fixed point theorems for different kinds of contractions in complex valued b-metric, like-metric spaces, and b-metric like spaces. Furthermore, we unveil a new definition for a class of metrics spaces,𝑏𝑣(𝜃) and we concentrate on the results of the fixed points. In the end, we use the results obtained to look into whether there is a solution to the integral equation of Fredholm and the local solution of ordinary differential equations in 𝑏𝑣(𝜃). Keywords: , b-metric like-space, Rational type contraction, cyclic-contractions, Complex-valued b-metric space,metric like-space, Set valued analysis, Multivalued mapping, Fixed point, Common fixed point.