Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations

Chapter 1. Introduction to FK spaces.- Chapter 2. Matrix Transformations.- Chapter 3. Some new sequence spaces of non-absolute type.- Chapter 4. Some non-classical sequence spaces.- Chapter 5. Measures of noncompactness.- Chapter 6. Application to compact matrix operators.- Chapter 7. Applications to infinite systems of differential equations.- Chapter 8. Applications to integral equations.

JÓZEF BANAS is professor of mathematics and chair at the Department of Mathematics in Rzeszow University of Technology, Poland. He is on the editorial committee of many journals of international repute: Commentationes Mathematicae (Polish Mathematical Society), Abstract and Applied Analysis (Hindawi Corporation), Journal of Inequalities and Applications (SpringerOpen), World Scientific Journal (Hindawi Corporation), Mathematica Applicanda (section: Mathematical Economics) and many others. Prof. Banas is also editor-in-chief of the Journal of Mathematics and Applications, Rzeszow. He has over 140 published research papers to his credit in journals such as Journal of Integral Equations and Applications, Rocky Mountain Journal of Mathematics, Proceedings of AMS, Journal of Mathematical Analysis and Applications, Applied Mathematics and Computation, Bulletin of the London Mathematical Society, Nonlinear Analysis, Abstract and Applied Analysis, among others. Prof. Banas is also coauthor of two books: Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics 60, Marcel Dekker, New York and Basel, 1980 (with K. Goebel) and Bounded Variation and Around, De Gruyter Series in Nonlinear Analysis and Applications 17, Walter de Gruyter, Berlin/Boston 2014 (with J. Appell and N. Merentes). His fields of interest include geometry of Banach spaces, measures of noncompactness, nonlinear differential and integral equations and applications of mathematics in economics. Professor J. Banas is a Supervisor of 10 PhD theses in mathematics.M. MURSALEEN is professor of mathematics at Aligarh Muslim University, Aligarh. Earlier, he worked as professor of mathematics at King Abdulaziz University, Jeddah, Saudi Arabia, during 2004-2006. An active researcher, Prof. Mursaleen has authored two books and five book chapters, in addition to his contributions to 190 research papers to various international journals such as Proc. Amer. Math. Soc., Quarterly J. Math.

"This book deals with some aspects of the theory of sequence spaces and operators acting between them. ... The book consists of eight chapters. Each chapter contains exercises and references. ... the book will be useful for all specialists in functional analysis since it contains a lot of new and interesting results." (P. P. Zabre ko, Mathematical Reviews, August, 2015)

"This is one of few books out there in which various types of measures of noncompactness are covered so extensively with the inclusion of the applications to compact matrix operators, infinite systems of differential equations and integral equations. ... The presentation is clear and self-contained throughout the entire treatment. Proofs of the main results are detailed and elegant. The book is suitable for graduate students and researchers with interest in generalized compactness methods for solving differential and integral equations." (Dhruba Adhikari, zbMATH 1323.47001, 2015)