6533b82bfe1ef96bd128e0e2

RESEARCH PRODUCT

Turán type inequalities for generalized inverse trigonometric functions

Barkat Ali BhayoMatti VuorinenÁRpád Baricz

subject

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-concavityMathematics

description

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.

yearjournalcountryeditionlanguage
2013-05-04Filomat
https://doi.org/10.2298/fil1502303b