Some fixed point theorems on dislocated metric spaces

This thesis consists of four sections. In the first section, basic concepts of metric spaces and various metric examples are given. Also sequence, continuity, convergence are introduced. Concepts of Cauchy sequence and complete metric space are recalled and some essential theorems are stated and proved. Subsequently concepts of fixed point, lipschitz condition, contraction mapping, contractive mapping, nonexpansive mapping are giving. Theorems and various examples are supported. Banach contraction mapping principles are stated and proved. An example are giving. Lastly application of linear equations of contraction mapping principles are given.In the second section, some essential definitions and theorems of dislocated metric spaces are giving. Also some fixed point theorems of dislocated metric spaces are examined and supported by examples of theorems.In the third section, concepts of neighborhoods, -open ball, d-membership relation, d-neighbourhood system, d-topological spaces, d-convergence, d-continuity, dislocation function in dislocated topology are introduced and some theorems with examples are giving.In the fourth section, some essential definitions and theorems of dislocated quasi metric spaces are giving. Subsequently some fixed point theorems of dislocated quasi metric spaces are examined. Finally we define the notion of a coupled fixed point and introduce coupled coincidence fixed point theorem in dislocated quasi metric spaces. Also we give an example to validate our main theorem and a corollary of the main result.