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Functional Equations and Inequalities in Several Variables

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 376/5 ( reviews)

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Book Synopsis Functional Equations and Inequalities in Several Variables by : Stefan Czerwik

Download or read book Functional Equations and Inequalities in Several Variables written by Stefan Czerwik. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with ? for the first time in the mathematical literature. The book contains many fresh results concerning those problems.

Functional Equations in Several Variables

1989 Mathematics
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Release : 1989
Genre : Mathematics
Kind : eBook
Book Rating : 765/5 ( reviews)

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Book Synopsis Functional Equations in Several Variables by : J. Aczél

Download or read book Functional Equations in Several Variables written by J. Aczél. This book was released on 1989. Available in PDF, EPUB and Kindle. Book excerpt: This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not at the expense of theory, so they have kept the prerequisites to a minimum.

Stability of Functional Equations in Several Variables

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 903/5 ( reviews)

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Book Synopsis Stability of Functional Equations in Several Variables by : D.H. Hyers

Download or read book Stability of Functional Equations in Several Variables written by D.H. Hyers. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co author and friend Professor Donald H. Hyers passed away.

An Introduction to the Theory of Functional Equations and Inequalities

2009-03-12 Mathematics
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Release : 2009-03-12
Genre : Mathematics
Kind : eBook
Book Rating : 491/5 ( reviews)

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Book Synopsis An Introduction to the Theory of Functional Equations and Inequalities by : Marek Kuczma

Download or read book An Introduction to the Theory of Functional Equations and Inequalities written by Marek Kuczma. This book was released on 2009-03-12. Available in PDF, EPUB and Kindle. Book excerpt: Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)

Functional Equations And Inequalities: Solutions And Stability Results

2017-03-20 Mathematics
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Release : 2017-03-20
Genre : Mathematics
Kind : eBook
Book Rating : 628/5 ( reviews)

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Book Synopsis Functional Equations And Inequalities: Solutions And Stability Results by : John Michael Rassias

Download or read book Functional Equations And Inequalities: Solutions And Stability Results written by John Michael Rassias. This book was released on 2017-03-20. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.

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