New fixed point results in partial b-metric spaces

Abstract

Fixed point analysis is one of the most effective and valuable methods in modern mathematics, and it can be considered a major subject of nonlinear analysis, which Banach began in 1922. In this thesis, fundamental idea of fixed point analysis has been generalized by expanding the domain of the contraction as a new contraction supported by a weak triangular α-admissible mapping with regards to η and C−class function in the class of partial b−metric spaces on a set W. For these novel contraction mappings, we have proved the existence and uniqueness of the fixed point results. We have presented an example and application as a result of our main theorems to establish the validity of our fixed point results in the partial b−metric spaces to generalize and enhance various studies in the literature.