A Study on Fixed Point and Common Coupled Fixed Point and its Applications

Abstract

The primary objective of this thesis is to explore fixed point theorems and common coupled newlinefixed point theorems for various orthogonal contraction mappings in different orthogonal newlinemetric spaces, while tailoring practical applications to specific scenarios. newlineIn chapter 1, we establish fixed point results for an orthogonal extended newlineinterpolative Ciric-Reich-Rus type and#968;F -contraction mapping in orthogonal complete newlineb -metric spaces, accompanied by an example to reinforce our main conclusions. newlineAdditionally, we provide an application of the fixed point results to derive analytical newlinesolutions for integral equations. newlineIn chapter 2, we develop fixed point theorems for orthogonal hybrid interpolative newlineReich-Istrand#728;atescu type contraction mappings in orthogonal complete b -metric spaces, newlineeffectively expanding this class. Examples are presented to illustrate the significant work newlinethat underpins our key results. Finally, we offer an application to examine the existence newlineand uniqueness of a solution to an integral equation, supplemented by numerical results newlinethat demonstrate its effectiveness. newlineIn chapter 3, we establish various fixed point theorems related to different types of newlineorthogonal (and#981;,and#186315;) contractions in orthogonal Branciari b -metric spaces. We provide an newlineexample to strengthen the existing results, emphasizing our main findings. Furthermore, newlinewe offer an application that clarifies the existence and uniqueness of integral equation newlinesolutions, concluding with numerical results that contrast with the analytical solutions. newlineIn chapter 4, we prove a fixed point theorem using orthogonal Geraghty-type and#945; - newlineadmissible contraction mappings in orthogonal complete Branciari b -metric spaces newline