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A Catalogue of Help and Help-type Integral and Series Inequalities

  • M. Benammar
  • C. Bennewitz
  • M. J. Beynon
  • B. M. Brown
  • N. G. J. Dias
  • W. D. Evans
  • W. N. Everitt
  • V. G. Kirby
  • L. L. Littlejohn
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

This catalogue of the HELP and HELP-type integral and series inequalities records the contributions made to this area of analytic inequalties from the years 1971–1996. The original HELP integral inequality came from the results of Hardy and Littlewood in one of their seminal papers, in this case written in 1932. The main analytic tools for the study of these inequalities are the properties of linear, ordinary, self-adjoint differential operators, and the properties of the Titchmarsh-Weyl / Hellinger-Nevanlinna m-coefficient and its ramifications. It is appropriate then, that this catalogue records some of the many distinguished contributions made to mathematical analysis in the first half of this century, by these named mathematicians. Likewise it is appropriate that this catalogue is dedicated to D.S. Mitrinović whose contributions to the study and recording of analytic inequalities in the second half of this century, are now legendary.

Key words and phrases

Integral inequalities Titchmarsh-Weyl m-coefficient Ordinary differential and difference operators 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • M. Benammar
    • 1
  • C. Bennewitz
    • 2
  • M. J. Beynon
    • 3
  • B. M. Brown
    • 4
  • N. G. J. Dias
    • 5
  • W. D. Evans
    • 6
  • W. N. Everitt
    • 7
  • V. G. Kirby
    • 8
  • L. L. Littlejohn
    • 9
  1. 1.Science Wing, Air College (Dafra)Abu DhabiUnited Arab Emirates
  2. 2.Mathematical InstituteUniversity of LundLundSweden
  3. 3.Cardiff Business SchoolCardiffWales, UK
  4. 4.Department of Computer ScienceUniversity of Wales CardiffCardiffWales, UK
  5. 5.Department of MathematicsUniversity of KelaniyaKelaniyaSri Lanka
  6. 6.Mathematical InstituteSchool of Mathematics, University of Wales CardiffCardiffWales, UK
  7. 7.School of Mathematics and StatisticsUniversity of BirminghamEdgbaston, BirminghamEngland, UK
  8. 8.Department of MathematicsDublin City UniversityDublin 9Ireland
  9. 9.Department of Mathematics and StatisticsUtah State UniversityLoganUSA

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