This book offers a comprehensive exploration of the dynamic intersection between geometry and optimization. It delves into the intricate study of Hermite-Hadamard inequalities, Hilbert type integral inequalities, and variational inequalities, providing a rich tapestry of theoretical insights and practical applications.

Readers will encounter a diverse array of topics, including the bounds for the unweighted Jensen's gap of absolutely continuous functions and the properties of Barrelled and Bornological locally convex spaces. The volume also covers advanced subjects such as multiobjective mixed-integer nonlinear optimization and optimum statistical analysis on sphere surfaces. Contributions from eminent scholars provide a deep dive into C*-ternary biderivations, Erds-Szekeres products, and variational principles, making this book a must-read for those seeking to expand their understanding of these complex fields.

Ideal for researchers and scholars in mathematics and optimization, this volume is an invaluable resource for anyone interested in the latest developments in geometry and nonconvex optimization. Whether you are a seasoned academic or a graduate student, this book will enhance your knowledge and inspire further research in these fascinating domains.

Contributions include both survey and research papers which reach several levels of readership Focuses on very vibrant and relevant subjects of active research Features theory, methods and results in a broad spectrum of applicable areas

Autorentext
Panos Pardalos is a Distinguished Emeritus Professor in the Department of Industrial and Systems Engineering at the University of Florida, and an affiliated faculty of Biomedical Engineering and Computer Science & Information & Engineering departments. He is a world-renowned leader in Global Optimization, Mathematical Modeling, Energy Systems, Financial applications, and Data Sciences. He is a Fellow of AAAS, AAIA, AIMBE, EUROPT, and INFORMS and was awarded the 2013 Constantin Caratheodory Prize of the International Society of Global Optimization. In addition, Panos Pardalos has been awarded the 2013 EURO Gold Medal prize bestowed by the Association for European Operational Research Societies. This medal is the preeminent European award given to Operations Research (OR) professionals for "scientific contributions that stand the test of time." He has also been awarded the prestigious Humboldt Research Award (20182019). The Humboldt Research Award is granted in recognition of a researcher's entire achievements to date fundamental discoveries, new theories, insights that have had significant impact on their discipline. ****Themistocles M. Rassias is Emeritus professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 47.

Inhalt

Preface.- Chapter 1 Hermite-Hadamard Like Inequalities Involving Generalized Bi-Convex Functions.- Chapter 2 Some properties of Barrelled and of Bornological locally convex spaces over an arbitrary complete valued field.- Chapter 3 Bounds for the Unweighted Jensen's Gap of Absolutely Continuous Functions.- Chapter 4 Test Instances for Multiobjective Mixed-Integer Nonlinear Optimization.- Chapter 5 A trace operator for weighted Sobolev spaces.- Chapter 6 Common fixed point results for Meir-Keeler type contraction mappings.- Chapter 7 Optimum Statistical Analysis on Sphere Surface.- Chapter 8 New Generalized Ostrowski Type Fractional Integral Inequalities.- Chapter 9 Genaralized Fractional Hilbert Type Integral Inequalities in Banach Spaces.- Chapter 10 Ternary derivation-homomorphism functional inequalities.- Chapter 11 C*-ternary biderivations and C*-ternary bihomomorphisms.- Chapter 12 A Survey of Erds-Szekeres Products.- Chapter 13 Recent developments in general quasi variational inequality.- Chapter 14 General Variational Inequalities and Optimization.- Chapter 15 Characterizations and Set Theoretic Properties of Some Generalized Open and Fat Sets in Relator Spaces.- Chapter 16 Direct Continuity Properties of Relations in Relator Spaces.- Chapter 17 Variational Principles and Fixed Points in Symmetric Structures.- Chapter 18 Sequential Coercivity over Q-Ordered Q-Metric Spaces.- Chapter 19 A Hardy-Hilbert's Integral Inequality with the Internal Variables Involving Two Derivative Functions.