• Title, Summary, Keyword: Ostrowski type inequality

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CERTAIN GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS

  • Choi, Junesang;Set, Erhan;Tomar, Muharrem
    • Communications of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.601-617
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    • 2017
  • We give a function associated with generalized Ostrowski type inequality and its integral representation for local fractional calculus. Then, using this function and its integral representation, we establish several inequalities of generalized Ostrowski type for twice local fractional differentiable functions. We also consider some special cases of the main results which are further applied to a concrete function to yield two interesting inequalities associated with two generalized means.

ON THE OSTROWSKI INEQUALITY FOR THE RIEMANN-STIELTJES INTEGRAL ${\int}_a^b$ f (t) du (t), WHERE f IS OF HÖLDER TYPE AND u IS OF BOUNDED VARIATION AND APPLICATIONS

  • DRAGOMIR, S.S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.1
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    • pp.35-45
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    • 2001
  • In this paper we point out an Ostrowski type inequality for the Riemann-Stieltjes integral ${\int}_a^b$ f (t) du (t), where f is of p-H-$H{\ddot{o}}lder$ type on [a,b], and u is of bounded variation on [a,b]. Applications for the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also given.

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