Bøker av Qamrul Hasan (Aligarh Muslim University Ansari

The book is designed for undergraduates, graduates, and researchers of mathematics studying fixed point theory or nonlinear analysis. It deals with the fixed point theory for not only single-valued maps but also set-valued maps. The text is divided into three parts: fixed point theory for single-valued mappings, continuity and fixed point aspects of set-valued analysis, and variational principles and their equilibrium problems. It comprises a comprehensive study of these topics and includes all important results derived from them. The applications of fixed point principles and variational principles, and their generalizations to differential equations and optimization are covered in the text. An elementary treatment of the theory of equilibrium problems and equilibrium version of Ekeland's variational principle is also provided. New topics such as equilibrium problems, variational principles, Caristi's fixed point theorem, and Takahashi's minimization theorem with their applications are also included.

Until now, no book addressed convexity, monotonicity, and variational inequalities together. This book covers all three topics, including new variational inequality problems defined by a bifunction. It deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The first part of the book focuses on generalized convexity and generalized monotonicity. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings.