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.

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.

S. A. Mohiuddine is a full Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. An active researcher, he has co-authored 5 books: Convergence Methods for Double Sequences and Applications (Springer, 2014), Advances in Summability and Approximation Theory (Springer, 2018), Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences (CRC Press, Taylor & Francis Group, 2021), Approximation Theory, Sequence Spaces, and Applications (Springer, 2022), Sequence Space Theory with Applications (CRC Press, Taylor & Francis Group, 2023), and a number of chapters in numerous edited books. More than 170 research papers and various leading journals, bear his name.

Mohiuddine is the referee of scientific journals and a member of the editorial boards of those journals, various international scientific bodies and organizing committees. He has visited international universities, including Imperial College London, UK, and served as a guest editor for a number of special journals’ issues. His research interests are: sequence spaces, statistical convergence, matrix transformation, measures of non-compactness and approximation theory. His name has appeared in the prestigious list of World's Top 2% Scientists, compiled by Stanford University in California, USA, via Scopus data provided by Elsevier, for four consecutive years from 2020-2023.

M. Mursaleen, since 1982, has served at Aligarh Muslim University from lecturer to full Professor. From 2915 to 2018, he was Chairman of the Department of Mathematics. He has published 9 books, published more than 400 research papers in several highly reputed journals, and besides Masters’ students, has guided 21 Ph.D. students.

Mursaleen has been a reviewer for various international scientific journals and is a member of numerous editorial boards for various international scientific journals. He has received a number of awards