Search results for "Mathematics::Classical Analysis and ODEs"

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Functional inequalities for generalized inverse trigonometric and hyperbolic functions

2014

Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.

ta113Pure mathematicsGeneralized inverseBernoulli's inequalityGeneralized inverse trigonometric functions; Generalized inverse hyperbolic functions; Functional inequalities; Generalized hypergeometric 3F2 functionApplied MathematicsHyperbolic functionMathematics::Classical Analysis and ODEsHypergeometric distributionClausen functionMathematics - Classical Analysis and ODEsBounding overwatchClassical Analysis and ODEs (math.CA)FOS: MathematicsTrigonometry33B99 26D15 33C20 33C99AnalysisQuotientMathematicsJournal of Mathematical Analysis and Applications
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Fractional Hardy inequalities and visibility of the boundary

2013

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

visibility of the boundaryPure mathematicsMathematics::Functional AnalysisInequalityfractional Hardy inequalitiesGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsVisibility (geometry)46E35 (26D15)Open setMathematics::Classical Analysis and ODEsOrder (ring theory)Boundary (topology)01 natural sciences010101 applied mathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsExposition (narrative)media_common
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