Fixed Point Theory, Variational Analysis, and Optimization

Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis?fixed point theory, variational inequalities, and vector optimization?but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions involving differentiable or directionally differentiable functions. This essential reference supplies both an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. Packed with detailed proofs and bibliographies for further reading, the text:

• Examines Mann-type iterations for nonlinear mappings on some classes of a metric space
• Outlines recent research in fixed point theory in modular function spaces
• Discusses key results on the existence of continuous approximations and selections for set-valued maps with an emphasis on the nonconvex case
• Contains definitions, properties, and characterizations of convex, quasiconvex, and pseudoconvex functions, and of their strict counterparts
• Discusses variational inequalities and variational-like inequalities and their applications
• Gives an introduction to multi-objective optimization and optimality conditions
• Explores multi-objective combinatorial optimization (MOCO) problems, or integer programs with multiple objectives

Fixed Point Theory, Variational Analysis, and Optimization is a beneficial resource for the research and study of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.

Common Fixed Points in Convex Metric Spaces. Fixed Points of Nonlinear Semigroups in Modular Function Spaces. Approximation and Selection Methods for Set-Valued Maps and Fixed Point Theory. Convexity, Generalized Convexity, and Applications. New Developments in Quasiconvex Optimization. An Introduction to Variational-Like Inequalities. Vector Optimization: Basic Concepts and Solution Methods. Multi-Objective Combinatorial Optimization.

Saleh Abdullah R. Al-Mezel is a full professor of mathematics at King Abdulaziz University, Jeddah, Saudi Arabia and the vice president for academic affairs at the University of Tabuk, Saudi Arabia. He holds a B.Sc from King Abdulaziz University; an M.Phil from Swansea University, Wales; and a Ph.D from Cardiff University, Wales. He possesses over ten years of teaching experience and has participated in several sponsored research projects. His publications span numerous books and international journals.

Falleh Rajallah M. Al-Solamy is a professor of mathematics at King Abdulaziz University, Jeddah, Saudi Arabia and the vice president for graduate studies and scientific research at the University of Tabuk, Saudi Arabia. He holds a B.Sc from King Abdulaziz University and a Ph.D from Swansea University, Wales. A member of several academic societies, he possesses over 7 years of academic and administrative experience. He has completed 30 research projects on differential geometry and its applications, participated in over 14 international conferences, and published more than 60 refereed papers.

Qamrul Hasan Ansari is a professor of mathematics at Aligarh Muslim University, India, from which he also received his M.Phil and Ph.D. He has co/edited, co/authored, and/or contributed to 8 scholarly books. He serves as associate editor of the Journal of Optimization Theory and Applications and the Fixed Point Theory and Applications, and has guest-edited special issues of several other journals. He has more than 150 research papers published in world-class journals and his work has been cited in over 1,400 ISI journals. His fields of specialization and/or interest include nonlinear analysis, optimization, convex analysis, and set-valued analysis.