Naslov
Extension of Karamata inequality for generalized inverse trigonometric functions

Autori
Baricz, Arpad ; Poganj, Tibor

Izvornik
Studia Universitatis Babeş-Bolyai Mathematica (0252-1938) 60 (2015), 3; 379-384

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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