0000000000681349
AUTHOR
Barkat Ali Bhayo
Turán type inequalities for generalized inverse trigonometric functions
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.
Functional inequalities for generalized inverse trigonometric and hyperbolic functions
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.
On Carlson"s and Shafer"s inequalities
In this paper the authors re ne the Carlson"s inequalities for inverse cosine function, and the Shafer"s inequalities for inverse tangent function.
On some inequalities for the identric, logarithmic and related means
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.