0000000000681350

AUTHOR

ÁRpád Baricz

showing 2 related works from this author

Turán type inequalities for generalized inverse trigonometric functions

2013

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.

Bernstein functionsPure mathematicsTurán-type inequalitiesGeneralized inverseSeries (mathematics)General Mathematics33C99 33B99ta111Hyperbolic functionMathematics::Classical Analysis and ODEsInverseEigenfunctions of p-LaplacianEigenfunctionRamanujan's sumGeneralized trigonometric functionsymbols.namesakeDigamma functionMathematics - Classical Analysis and ODEsCompletely monotone functionsLog-convexitysymbolsTrigonometric functionsLog-concavityMathematicsFilomat
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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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