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Application of Davies–Petersen Lemma

In: Differential and Integral Inequalities

Author

Listed:
  • Manish Kumar

    (Birla Institute of Technology and Science-Pilani)

  • R. N. Mohapatra

    (University of Central Florida)

Abstract

In this paper we have shown how use of a simple lemma first proved by Davies and Petersen and later extended by Mohapatra and Russell can be used effectively to prove three main results which can yield integral inequalities of Hardy and Copson. We have also shown how those results can be used to obtain many known results obtained by Levinson, Pachpatte, Chan, etc. by carefully manipulating these three theorems. A look at this paper will also reveal that there can be simple proofs of sophisticated results after they have been proved by exploiting the important points that make things work. It does not take away the value of the original contributions. We have also mentioned that it has not been possible to deduce other known results by using our results.

Suggested Citation

  • Manish Kumar & R. N. Mohapatra, 2019. "Application of Davies–Petersen Lemma," Springer Optimization and Its Applications, in: Dorin Andrica & Themistocles M. Rassias (ed.), Differential and Integral Inequalities, pages 549-568, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-27407-8_19
    DOI: 10.1007/978-3-030-27407-8_19
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    Keywords

    26 D15;

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving

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