Fixed Point Theorems For Self-mappings Research Articles

Common fixed point theorems for C-class functions in b-metric spaces with application

In this paper, we establish the existence and uniqueness of common fixedpoint theorems for self mappings satisfying the common limit range property with re-spect to mappings S and T and common (E.A)-property via the concept of C-classfunctions in b-metric spaces. We furnish two examples to validate our results. Our re-sults improve various results appeared in the current literature. As an application, Weprovide the existence of a solution of an integral equations.

Common fixed point theorem for C-class functions in complete metric spaces with application

In this paper, we establish the existence and uniqueness of common fixed point theorem for self mappings satisfying contractive condition of integral type via the concept of C-class functions in complete metric spaces. Further, we furnish an example to validate our result. Our result improves various results in the current literature. Towards the end, the existence and uniqueness of common solutions for system of functional equations arising in dynamic programming are discussed as an application of our main result.

Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

Fixed-Point Theorem for Isometric Self-Mappings

In this paper, we derive a fixed-point theorem for self-mappings. That is, it is shown that every isometric self-mapping on a weakly compact convex subset of a strictly convex Banach space has a fixed point.

Fixed points for generalized contractions and applications to control theory

The concepts of “weak/strong topological contraction” and a generalization of Banach contraction mappings called “ p -contraction” are introduced and used to prove fixed point theorems for self-mappings from a topological/metric space into itself satisfying topological contraction/metric p -contraction, respectively. Certain non-linear integral equations defined on C [ a , b ] satisfying generalized Lipschitzian conditions can easily be solved by applying these theorems. In the sequel, we shall study the possibility of optimally controlling the solution of the ordinary differential equation via dynamic programming.