Studies on Fixed Point Theorems in Different Types of Contraction Mappings

Abstract

This thesis work investigates the existence and uniqueness of fixed point and approximate newlinefixed point theorems for self-mappings and non-self mappings within the settings of metric newlinespace, b-metric space, and orthogonal b-metric space. We establish fixed point results newlineusing and#945; -admissible mappings in conjunction with newly defined control functions. The newlineresearch also explores the strong convergence of new iterative procedures utilizing and#945; - newlineadmissible contraction mappings, with applications to integral equations. newlineFurther, we examine fixed point theorems involving distinct contractions in b-metric newlinespace and 2-metric space, utilizing generalized convex contraction mappings, and apply newlinethese results to solve integral equations. The study extends to orthogonal b-metric space, newlinewhere fixed point theorems using orthogonal Z -contraction mappings are demonstrated. newlineWe also obtain fixed point theorems for self-mappings using the altering distance function newlineunder convincing contraction conditions in orthogonal metric space, introducing a novel newlineconcept newline