Handbook of Functional Equations

Functional Inequalities

  • Themistocles M. Rassias

Part of the Springer Optimization and Its Applications book series (SOIA, volume 95)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vandanjav Adiyasuren, Tserendorj Batbold
    Pages 1-13
  3. Marta Bryla, Andrei V. Krupoderov, Alexey A. Kushunin, Vladimir Mityushev, Michail A. Zhuravkov
    Pages 15-42
  4. Pietro Cerone, Sever S. Dragomir, Eder Kikianty
    Pages 57-73
  5. Iulia Costin, Gheorghe Toader
    Pages 105-127
  6. P. Daniele, S. Giuffè, M. Lorino, A. Maugeri, C. Mirabella
    Pages 129-146
  7. Tamás Glavosits, Árpád Száz
    Pages 161-208
  8. N. K. Govil, Q. M. Tariq
    Pages 209-245
  9. Christos P. Kitsos, Thomas L. Toulias
    Pages 281-313
  10. Muhammad A. Noor, Themistocles M. Rassias
    Pages 407-417

About this book


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.



Cauchy equation Hosszu’s functional equation Jensen’s functional equation Lobachevskii’s functional equation Ulam stability functional equations handbook

Editors and affiliations

  • Themistocles M. Rassias
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-1246-9
  • Copyright Information Springer Science+Business Media, LLC 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1245-2
  • Online ISBN 978-1-4939-1246-9
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • About this book