Search results for "generalized trigonometric"

showing 2 items of 2 documents

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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Logarithmic mean inequality for generalized trigonometric and hyperbolic functions

2015

In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean. peerReviewed

generalized convexitygeneralized trigonometricinequalitieslogarithmic meanhyperboliset funktiot
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