Fixed Point Results for Contraction Mapping Concerning with Metric Spaces

Abstract

Mathematics may be used to decode any problem, regardless of its field, and a correct solution can be offered with a rigorous logic rationale and analysis. With the use of a mathematical tool, we can think more clearly and create original theories, justifications, and approaches to get the greatest outcome. Any problem relating to science, technology, economics, social science, medical, or even languages can be fitted with a proper mathematical framework, and a flawless solution can be attained. quotFixed point theory,quot the most fascinating and useful mathematical tool, has been emphasized for its applications in almost every discipline, including engineering, technology, and even basic research. Additionally, this platform has been made available to increase the capacity for idea generation. newlineOur present piece of work is divided into seven sections 4.1 to 4.7. newlineSection 4.1 deals with the study of fixed-point theorems for Rational Type Contraction in Controlled Metric Spaces. In this section, we present some fixed point theorems for mappings involving rational expressions in the context of complete controlled metric spaces. Our result extends and generalizes some well-known results in the literature. We also provide examples to show significance of the obtained results involving rational type contractive conditions. We furnish an example to demonstrate the validity of the hypotheses of generality of our result. newlineSection 4.2 is dedicated to Fixed Point Results of Dass and Gupta Rational Type Contraction in A_b-Metric Spaces. We define Dass and Gupta s rational contraction in the context of A_b-metric spaces and establish some fixed point theorems to elaborate, generalize and synthesize several known results in the literature. Finally, the example is presented to support the new theorem proved. newlineSection 4.3 is completely devoted to the study of fixed-point Theorems for Expansive Type Mapping on F-Cone Metric Spaces. In this section, inspired and encouraged by the previous works, to prove some fixed-point theorems for expa