engleski

Extension of Karamata inequality for generalized inverse trigonometric functions

Discussing Ramanujan's Question 294, Karamata established the inequality \[ (log x)/(x-1) \leq (1+\sqrt[3]{; ; ; ; ; x}; ; ; ; ; )/(x+\sqrt[3])\] for all $x>0, x\neq 1$ which is the cornerstone of this paper. We generalize the above inequality transforming into terms of arctan and artanh. Moreover, we expand the established result to the class of generalized inverse p- trigonometric arctan_p and to hyperbolic artanh_p functions.

Karamata inequality ; Ramanujan's question 294 ; Zero-balanced hypergeometric functions ; Generalized inverse trigonometric functions ; Rational upper bounds.

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