Measure of Noncompactness, Fixed Point Theorems, and Applications

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.

Table of Contents:
1. The existence and numerical solution of functional integral equation via coupled fixed point theorem, measure of non-compactness and iterative algorithm. 2. Applications of measure of non-compactness and Petryshyn's fixed-point theorem for a class of functional integral equations in a Banach algebra.3. Some Darbo fixed point theorems and solutions of the implicit fractional integral equation. 4. A survey on recent best proximity point results using measure of noncompactness and applications.5. A Petryshyn based approach to the existence of solutions for Volterra functional integral equations with Hadamard-type fractional integrals.6. Coupled fixed point theorem and measure of noncompactness for existence of solution of functional integral equations system and iterative algorithm to solve it. 7. Optimum solution of integral equation via measure of noncompactness. 8. Approximate finite dimensional additive mappings in modular spaces by fixed point method. 9. Ulam stability results of the quadratic functional equation in Banach space and multi-normed space by using direct and fixed point methods.10. Solution of simultaneous nonlinear integral equations by generalized contractive condition. 11. Compactness via Hausdor measure of non-compactness on q-Pascal difference sequence spaces.