This book presents original research on the theory of positive operators, alongside fixed-point theorems and their diverse applications. It introduces various positive operators and explores their approximation properties, including Korovkin-type theorems, Voronovskaja-type results, convergence rate, and other related findings. Additionally, the book addresses the existence of solutions for various differential and integral equations in different Banach spaces by using Darbo-type fixed-point theorems. This book also presents an interplay between positive operators and fixed-point theory. Each chapter is self-contained, addressing a current problem and outlining solutions and potential applications. The chapters provide sufficient background to ensure that new definitions and results can be understood independently.

Contains original research on the theory of positive operators as well as fixed-point theorems and applications Discusses the existence of solutions of several kinds of differential and integral equations in various Banach spaces Introduces some positive operators and studies their approximation properties

Autorentext

S. A. Mohiuddine is a full professor at the Department of General Required Courses, Mathematics, The Applied College, King Abdulaziz University, Jeddah, Saudi Arabia. As an active researcher, he has co-authored five books and a number of chapters in several edited book and has contributed more than 150 research papers to various leading journals. He is the referee of many scientific journals and member of the editorial board of various scientific journals, international scientific bodies and organizing committees. He has visited several international universities including Imperial College London, UK. He was a guest editor of a number of special issues in some journal. His name has been appeared in the list of World's Top 2% Scientists (for the three consecutive years 2020-2022) prepared by Stanford University, California, through Scopus data provided by Elsevier.

Anupam Das is an associate professor at the Department of Mathematics, Cotton University, Guwahati, Assam, India. Earlier, he worked as an assistant professor in the Department of Mathematics, Rajiv Gandhi University, Doimukh, Arunachal Pradesh, India. He received his Ph.D. in Mathematics from the Department of Mathematics, Rajiv Gandhi University. His research interests include summability theory, fixed point theory, best proximity point theory, fractional integral, and differential equations. He has published more than 40 articles in various international journals. He has successfully guided a Ph.D. student in the area of fixed point theory.

Dragan Djordjevic is Full Professor in the Department of Mathematics, Faculty of Sciences and Mathematics, University of Nis, Serbia, since 2006, which he joined in 1992. Earlier, he was the Dean of the Faculty of Sciences and Mathematics and a member of several scientific boards of the University of Nis (Senat, Scientific Council for Sciences and Mathematics), Ministry of Education, Science and Technological Development of Serbia (Scientific Council for Mathematics, Mechanics and Computer Science, Head of the Council), as well as in the Republic of Serbia (National Council for Higher Education). He also was the Head and a member of several scientific projects financed by the Ministry of Education, Science and Technological Development of Serbia. He is a member and Vice-President of the Association Serbian Scientific Mathematical Society. He supervised 10 Ph.D. theses and published more than 130 scientific papers in reputed journals. His scientific work includes operator theory, with some aspects of functional analysis, linear algebra, general algebra and numerical analysis. He is a member of boards of some mathematical journals: Filomat (one of the Editors-in-Chief), Functional Analysis, Approximation and Computation (founder and Editor-in-Chief), Applied Mathematics and Computer Science (founder and one of the Editors-in-Chief), Advances in the Theory of Nonlinear Analysis and its Application (member of the board),Publications de l'Institute Mathematique (member of the board), and Advances in Operator Theory (member of the board).

Inhalt

Chapter 1 Convergence of a Class of SzaszKantorovich Operators based on 2D Appell Polynomials .- Chapter 2 Convergence Results for Nonlinear Generalized Bernstein-type Operators.- Chapter 3 Existence of Solutions for Infinite System of Nonlinear q -fractional Boundary-value Problem via Generalized Darbo's Fixed-point Theorem.