Hassnain, Syed Irtaza. The existence of solutions for nonlinear implicit integral and matrix equations involving new rational contraction mappings. Doctoral Degree(Mathematics). Thammasat University. Thammasat University Library. : Thammasat University, 2021.
The existence of solutions for nonlinear implicit integral and matrix equations involving new rational contraction mappings
Abstract:
One of the exciting topics in the fixed point theory is the existence theorem of fixed points of self-mappings on complete metric spaces. It depends on the behavior of the focussed mappings. Based on this reason, many mathematicians attempted to introduce several specific conditions for guaranteeing the existence of fixed points. The idea of the contractive condition is trendy to study in this direction. There are several famous types of mappings that satisfy interesting contractive conditions from the past to the present, such as Banach contraction mappings, Kannan contraction mappings, Chatterjea contraction mappings, Reich contraction mappings, weak contraction mappings in the sense of Berinde, rational type contraction mappings, and convex contraction mappings. This dissertation aims to investigate new types of contraction mappings covering all mentioned contraction mappings. Many illustrative examples are presented to demonstrate the applicability of our presented fixed point results. Finally, the existence and uniqueness of a solution for the functional integral and matrix equations are solved by using our main theoretical fixed point results
Thammasat University. Thammasat University Library