Convex Functions And Their Applications

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Convex Functions And Their Applications

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Author : Constantin Niculescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-11

Convex Functions And Their Applications written by Constantin Niculescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-11 with Mathematics categories.

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching interests intersect with the field of convexity. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Prékopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential equations and convex programming. Many results are new and the whole book reflects the authors’ own experience, both in teaching and research. The book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering and it can also be used for graduate courses.

Convex Functions And Their Applications

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Author : Constantin P. Niculescu
language : en
Publisher: Springer
Release Date : 2018-06-08

Convex Functions And Their Applications written by Constantin P. Niculescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-08 with Mathematics categories.

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises

Convex Functions And Their Applications

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Author : Constantin P. Niculescu
language : en
Publisher: Springer Nature
Release Date : 2025-03-11

Convex Functions And Their Applications written by Constantin P. Niculescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-11 with Mathematics categories.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems. To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics. Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.

Soc Functions And Their Applications

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Author : Jein-Shan Chen
language : en
Publisher: Springer
Release Date : 2019-02-11

Soc Functions And Their Applications written by Jein-Shan Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-11 with Business & Economics categories.

This book covers all of the concepts required to tackle second-order cone programs (SOCPs), in order to provide the reader a complete picture of SOC functions and their applications. SOCPs have attracted considerable attention, due to their wide range of applications in engineering, data science, and finance. To deal with this special group of optimization problems involving second-order cones (SOCs), we most often need to employ the following crucial concepts: (i) spectral decomposition associated with SOCs, (ii) analysis of SOC functions, and (iii) SOC-convexity and -monotonicity. Moreover, we can roughly classify the related algorithms into two categories. One category includes traditional algorithms that do not use complementarity functions. Here, SOC-convexity and SOC-monotonicity play a key role. In contrast, complementarity functions are employed for the other category. In this context, complementarity functions are closely related to SOC functions; consequently, the analysis of SOC functions can help with these algorithms.

Advances In Mathematical Analysis And Its Applications

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Author : Bipan Hazarika
language : en
Publisher: CRC Press
Release Date : 2022-12-12

Advances In Mathematical Analysis And Its Applications written by Bipan Hazarika and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-12 with Mathematics categories.

Advances in Mathematical Analysis and its Applications is designed as a reference text and explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. It discusses theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some topics are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. Features: The book encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. It offers an understanding of research problems by presenting the necessary developments in reasonable details The book also discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems Contains applications on wavelets analysis and COVID-19 to show that mathematical analysis has interdisciplinary as well as real life applications. The book is aimed primarily at advanced undergraduates and postgraduate students studying mathematical analysis and mathematics in general. Researchers will also find this book useful.

Mathematical Analysis And Applications

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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-05-11

Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Mathematics categories.

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Asymptotic Characteristics Of Entire Functions And Their Applications In Mathematics And Biophysics

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Author : L.S. Maergoiz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Asymptotic Characteristics Of Entire Functions And Their Applications In Mathematics And Biophysics written by L.S. Maergoiz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics is the second edition of the same book in Russian, revised and enlarged. It is devoted to asymptotical questions of the theory of entire and plurisubharmonic functions. The new and traditional asymptotical characteristics of entire functions of one and many variables are studied. Applications of these indices in different fields of complex analysis are considered, for example Borel-Laplace transformations and their modifications, Mittag-Leffler function and its natural generalizations, integral methods of summation of power series and Riemann surfaces. In the second edition, a new appendix is devoted to the consideration of those questions for a class of entire functions of proximate order. A separate chapter is devoted to applications in biophysics, where the algorithms of mathematical analysis of homeostasis system behaviour, dynamics under external influence are investigated, which may be used in different fields of natural science and technique. This book is of interest to research specialists in theoretical and applied mathematics, postgraduates and students of universities who are interested in complex and real analysis and its applications.

Handbook Of Functional Equations

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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-11-18

Handbook Of Functional Equations written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-18 with Mathematics categories.

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Elementary Convexity With Optimization

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Author : Vivek S. Borkar
language : en
Publisher: Springer Nature
Release Date : 2023-06-26

Elementary Convexity With Optimization written by Vivek S. Borkar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-26 with Mathematics categories.

This book develops the concepts of fundamental convex analysis and optimization by using advanced calculus and real analysis. Brief accounts of advanced calculus and real analysis are included within the book. The emphasis is on building a geometric intuition for the subject, which is aided further by supporting figures. Two distinguishing features of this book are the use of elementary alternative proofs of many results and an eclectic collection of useful concepts from optimization and convexity often needed by researchers in optimization, game theory, control theory, and mathematical economics. A full chapter on optimization algorithms gives an overview of the field, touching upon many current themes. The book is useful to advanced undergraduate and graduate students as well as researchers in the fields mentioned above and in various engineering disciplines.

Integral Inequalities And Generalized Convexity

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Author : Shashi Kant Mishra
language : en
Publisher: CRC Press
Release Date : 2023-09-18

Integral Inequalities And Generalized Convexity written by Shashi Kant Mishra and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with Mathematics categories.

The book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus. The book contains integral inequalities of Hermite-Hadamard type, Hermite- Hadamard-Fejer type and majorization type for the generalized strongly convex functions. It presents Hermite-Hadamard type inequalities for functions defined on Time scales. Further, it provides the generalization and extensions of the concept of preinvexity for interval-valued functions and stochastic processes, and give Hermite-Hadamard type and Ostrowski type inequalities for these functions. These integral inequalities are utilized in numerous areas for the boundedness of generalized convex functions. Features: Covers Interval-valued calculus, Time scale calculus, Stochastic processes – all in one single book Numerous examples to validate results Provides an overview of the current state of integral inequalities and convexity for a much wider audience, including practitioners Applications of some special means of real numbers are also discussed The book is ideal for anyone teaching or attending courses in integral inequalities along with researchers in this area.