On the special form of integral convolution type inequality due to Walter and Weckesser View Full Text


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Article Info

DATE

2019-02

AUTHORS

Tomasz Małolepszy, Janusz Matkowski

ABSTRACT

Walter and Weckesser’s result (Aequationes Math 46:212–219, 1993), extending the Bushell–Okrasiński convolution type inequality (Bushell and Okrasiński in J Lond Math Soc (2) 41:503–510, 1990), gave some general conditions on the functions k:0,d→R and g:0,∞→R under which, for every increasing function f : 0,d→0,∞, the inequality ∫0xkx-sgfsds≤g∫0xfsds,x∈0,d,is satisfied. Applying the result on a simultaneous system of functional inequalities, we prove that if d>1, then, in general, both k and g must be power functions. More... »

PAGES

9-19

References to SciGraph publications

  • 2000. On the Best Constant in a Poincare-Sobolev Inequality in DIFFERENTIAL OPERATORS AND RELATED TOPICS
  • 1993-08. An integral inequality of convolution type in AEQUATIONES MATHEMATICAE
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00010-018-0576-1

    DOI

    http://dx.doi.org/10.1007/s00010-018-0576-1

    DIMENSIONS

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