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Frontiers in Functional Equations and Analytic Inequalities

  • George A. Anastassiou
  • John Michael Rassias
Book

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Jaeyoung Chung, John Michael Rassias, Bogeun Lee, Chang-Kwon Choi
      Pages 27-42
  3. Functional Equations

    1. Front Matter
      Pages 43-43
    2. K. H. Sabour, A. Charifi, S. Kabbaj
      Pages 93-111
    3. B. V. Senthil Kumar, S. Sabarinathan, M. J. Rassias
      Pages 143-152
    4. S. Tamilvanan, E. Thandapani, J. M. Rassias
      Pages 153-158
    5. Sandra Pinelas, V. Govindan, K. Tamilvanan
      Pages 159-181
    6. Ahmed Nuino, Muaadh Almahalebi, Ahmed Charifi
      Pages 183-193
    7. Murali Ramdoss, Ponmana Selvan Arumugam
      Pages 195-217
    8. Belaid Bouikhalene, Elhoucien Elqorachi
      Pages 219-235
    9. Douglas R. Anderson, Masakazu Onitsuka
      Pages 237-254
    10. A. Charifi, D. Zeglami, S. Kabbaj
      Pages 273-292
  4. Analytic Inequalities

    1. Front Matter
      Pages 293-293
    2. Tianzhou Xu, Yali Ding, John Michael Rassias
      Pages 309-323
    3. George A. Anastassiou
      Pages 325-355
    4. George A. Anastassiou
      Pages 371-422
    5. Eze R. Nwaeze, Delfim F. M. Torres
      Pages 423-434
    6. George A. Anastassiou
      Pages 435-468
    7. S. H. Saker, M. R. Kenawy, D. Baleanu
      Pages 489-510
    8. Soumia Touhami, Abdellatif Chaira, Delfim F.  M. Torres
      Pages 599-611
    9. Jadranka Mićić, Marjan Praljak
      Pages 651-676
    10. Shusen Ding, Dylan Helliwell, Gavin Pandya, Arthur Yae
      Pages 677-693
    11. Hamid Vosoughian, Sadegh Abbaszadeh, Maryam Oraki
      Pages 695-711
  5. Back Matter
    Pages 747-753

About this book

Introduction

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: 
  • Hyperstability of a linear functional equation on restricted domains
  • Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations
  • Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations
  • General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces
  • Stabilities of Functional Equations via Fixed Point Technique
  • Measure zero stability problem for the Drygas functional equation with complex involution
  • Fourier Transforms and Ulam Stabilities of Linear Differential Equations
  • Hyers–Ulam stability of a discrete diamond–alpha derivative equation
  • Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. 

The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book. 

Keywords

Functional Inequalities Functional Equations Polya Inequalities Operator Inequalities Opial Inequalities Gruss Inequalities

Editors and affiliations

  • George A. Anastassiou
    • 1
  • John Michael Rassias
    • 2
  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA
  2. 2.Pedagogical Department E. E., Section of Mathematics and InformaticsNational and Kapodistrian University of AthensAthensGreece

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