Extension of Karamata inequality for generalized inverse trigonometric functions
Keywords:
Karamata's inequality, Ramanujan's question 294, zero-balanced hypergeometric functions, generalized inverse trigonometric functions, rational upper bounds.Abstract
Discussing Ramanujan's Question 294, Karamata established the inequality …
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 arctanp and to hyperbolic artanhp functions.
Mathematics Subject Classification (2010): 26D99, 39B62, 39B72.
References
Baricz, A., Bhayo, B.A., Vuorinen, M., Tur_an type inequalities for generalized inverse trigonometric functions, Filomat, 29(2)(2015), 303-313.
Berndt, B.C., Choi, J., Kang, S.-Y., The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society, in Berndt, B. C., Gesztesy, F. (Eds.), "Continued Fractions: From Analytic Number Theory to Constructive Approximation" (Columbia, MO, 1998), 15-56, Contemp. Math., 236, Amer. Math. Soc., Providence, RI, 1999.
Bhayo, B.A., Vuorinen, M., On generalized trigonometric functions with two parameters, J. Approx. Theory, 164(2012), 1415-1426.
Karamata, J., Sur quelques problemes poses par Ramanujan, J. Indian Math. Soc. (N.S.), 24(1960), 343-365.
Lindqvist, P., Some remarkable sine and cosine functions, Ricerche di Matematica XLIV, (1995) 269-290.
Mitrinovic, D.S., Analiticke nejednakosti, Grad. evinska Knjiga, Beograd, 1970.
Ramanujan, S., Question 294, J. Indian Math. Soc., 3(1911), 128.
Simic, S., A solution of an old problem of Karamata, Publ. Inst. Math. (Beograd) (N.S.), 70(84)(2001), 19-25.
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