Some Fixed Point Theorems for Contractive Mappings In Complex Valued Partial b-Metric Spaces

The technique of fixed point is assumed a core and powerful tool in Nonlinear Functional Analysis because it plays an important role in pure and applied Mathematics. Fixed point theorem is the developments of new creative methods to use the fundamental tools of the functional analysis. Functional analysis embodies the abstract approach in analysis. It gives many fundamental notions relevant for the description, Analysis, Numerical Approximation, Medicinal Ecology, Agro industries and Computer Simulation process. It also discovers solutions to problems occurring in pure, applied and social sciences. In this way, Mathews introduced the notion of Partial Metric space as a part of the study of mentioned semantics of data flow networks related to Computer Science. There are many researchers extended the concept of Partial metric space such as Partial b-metric space, Complex Valued partial metric space, Fuzzy type Partial metric space and proved the existence of fixed point theorem via contraction mappings.