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Vector Variational Inequalities and Vector Optimization - Theory and Applications (Hardcover, 1st ed. 2018): Qamrul Hasan... Vector Variational Inequalities and Vector Optimization - Theory and Applications (Hardcover, 1st ed. 2018)
Qamrul Hasan Ansari, Elisabeth Kobis, Jen-Chih Yao
R5,905 Discovery Miles 59 050 Ships in 7 - 11 working days

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Nonlinear Analysis - Approximation Theory, Optimization and Applications (Paperback, Softcover reprint of the original 1st ed.... Nonlinear Analysis - Approximation Theory, Optimization and Applications (Paperback, Softcover reprint of the original 1st ed. 2014)
Qamrul Hasan Ansari
R3,738 Discovery Miles 37 380 Ships in 7 - 11 working days

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Topics in Fixed Point Theory (Paperback, Softcover reprint of the original 1st ed. 2014): Saleh Almezel, Qamrul Hasan Ansari,... Topics in Fixed Point Theory (Paperback, Softcover reprint of the original 1st ed. 2014)
Saleh Almezel, Qamrul Hasan Ansari, Mohamed Amine Khamsi
R3,215 Discovery Miles 32 150 Ships in 7 - 11 working days

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland's variational principle.

Topics in Fixed Point Theory (Hardcover, 2014 ed.): Saleh Almezel, Qamrul Hasan Ansari, Mohamed Amine Khamsi Topics in Fixed Point Theory (Hardcover, 2014 ed.)
Saleh Almezel, Qamrul Hasan Ansari, Mohamed Amine Khamsi
R3,807 Discovery Miles 38 070 Ships in 7 - 11 working days

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland's variational principle.

Recent Developments in Vector Optimization (Paperback, 2012 ed.): Qamrul Hasan Ansari, Jen-Chih Yao Recent Developments in Vector Optimization (Paperback, 2012 ed.)
Qamrul Hasan Ansari, Jen-Chih Yao
R3,757 Discovery Miles 37 570 Ships in 7 - 11 working days

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

Recent Developments in Vector Optimization (Hardcover, 2012): Qamrul Hasan Ansari, Jen-Chih Yao Recent Developments in Vector Optimization (Hardcover, 2012)
Qamrul Hasan Ansari, Jen-Chih Yao
R3,777 R2,989 Discovery Miles 29 890 Save R788 (21%) Ships in 12 - 17 working days

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one often encounters such kind of problems. The most important and difficult part in such problems is the conflict between various objectives and goals. In these problems, one has to find the minimum(or maximum) for several objective functions. Such problems are called vector optimization problems (VOP),multi-criteria optimization problems or multi-objective optimization problems. This volume deals with several different topics / aspects of vector optimization theory ranging from the very beginning to the most recent one. It contains fourteen chapters written by different experts in the field of vector optimization.

Metric Spaces - Including Fixed Point Theory and Set-valued Maps (Hardcover): Qamrul Hasan Ansari Metric Spaces - Including Fixed Point Theory and Set-valued Maps (Hardcover)
Qamrul Hasan Ansari
R534 Discovery Miles 5 340 Ships in 12 - 17 working days

"Metric Spaces" is intended for undergraduate students offering a course of metric spaces and post graduate students offering a course of nonlinear analysis or fixed point theory. The first six chapters cover basic concepts of metric spaces, separable spaces, compact spaces, connected spaces and continuity of functions defined on a metric space. Chapter seven is devoted to the metric fixed point theory. Banach contraction theorem and several of its generalizations along with their applications and Caristi's fixed point theorem are also given in this chapter. The introductory set-valued analysis with special emphysis on continuity and fixed point theory of set-valued maps is given in chapter eight. One of the most useful and important results from nonlinear analysis is Ekeland's variational principle. This principle along with several of its equivalent forms, Takahashi's minimization theorem, introduction of theory of equilibrium problems and the equilibrium version of Ekeland's variational principle and several of its equivalent forms are presented in the last chapter. This book will also be useful for researchers working in nonlinear analysis, optimization and theory of equilibrium problems.

Nonlinear Analysis - Approximation Theory, Optimization and Applications (Hardcover, 2014 ed.): Qamrul Hasan Ansari Nonlinear Analysis - Approximation Theory, Optimization and Applications (Hardcover, 2014 ed.)
Qamrul Hasan Ansari
R3,417 R2,795 Discovery Miles 27 950 Save R622 (18%) Ships in 12 - 17 working days

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Vector Variational Inequalities and Vector Optimization - Theory and Applications (Paperback, Softcover reprint of the original... Vector Variational Inequalities and Vector Optimization - Theory and Applications (Paperback, Softcover reprint of the original 1st ed. 2018)
Qamrul Hasan Ansari, Elisabeth Koebis, Jen-Chih Yao
R4,539 Discovery Miles 45 390 Out of stock

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Analysis and its Applications (Hardcover): Rais Ahmad, Qamrul Hasan Ansari, Mohammad Imdad Analysis and its Applications (Hardcover)
Rais Ahmad, Qamrul Hasan Ansari, Mohammad Imdad
R1,261 R1,178 Discovery Miles 11 780 Save R83 (7%) Out of stock

Of immense value to researchers and professionals working in the wide domain of analysis and its applications, this volume provides an informative discussion on the prevalent topics of analysis, discussing subjects like Nonlinear Analysis; Operator Theory; Fixed Point Theory; Set-valued Analysis; Variational Analysis (including Variational Inequalities) and many more.

Fixed Point Theory, Variational Analysis, and Optimization (Hardcover): Saleh Abdullah R. Al-Mezel, Falleh Rajallah M.... Fixed Point Theory, Variational Analysis, and Optimization (Hardcover)
Saleh Abdullah R. Al-Mezel, Falleh Rajallah M. Al-Solamy, Qamrul Hasan Ansari
R4,336 Discovery Miles 43 360 Out of stock

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.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization (Hardcover): Qamrul Hasan Ansari, C. S.... Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization (Hardcover)
Qamrul Hasan Ansari, C. S. Lalitha, Monika Mehta
R4,321 Discovery Miles 43 210 Out of stock

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.

The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential.

The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential.

Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

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