Existence of fixed Point Results for Mappings in Metric Spaces

Abstract

newline The present thesis mainly involves fixed point results for various types of compatible mappings and weak commuting mappings that satisfy a generalized (and#968;,and#981;)-weak contraction involving cubic terms of distance functions. Some examples and applications are also provided to validate the obtained results in thesis. The present thesis is divided into six chapters. newline newlineChapter 1 is introductory. A generalized (and#968;,and#981;)-weak contraction involving cubic terms of distance functions is introduced. Using this condition some common fixed point theorems for various types of compatible mappings (type (A), type (B), type (C), type (P)), various types of compatible mappings (type (R), type (K), type (E)) and intimate mappings, weakly compatible mappings along with common limit range property, pointwise R-weakly commuting mappings are proved in Chapter 2, Chapter 3 and Chapter 4 respectively. Some relevant examples and applications are also discussed to validate the obtained results. newline newline In Chapter 5, a generalized (and#968;,and#981;)-weak integral contraction involving cubic terms of distance functions is introduced and using this condition some common fixed point theorems for various types of commuting mappings and subsequential continuous mappings, faintly compatible mappings are proved. As applications the obtained results are used to find common solution of functional equations arising in dynamic programming. Chapter 6 includes common fixed point theorems for families of weakly compatible mappings and weakly compatible mapping along with property (E. A). newline Finally, we give conclusion and scope for future works. The thesis ends with a Bibliography which includes several important works directly or indirectly associated with the research. newlineKeywords: Metric spaces; Fixed point; Compatible mappings; Variants of newline compatible mappings; Commuting mappings newline