Paper's Title:

Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions

Author(s):

P. Kórus, Z. Retkes

Institute of Applied Pedagogy,
Juhász Gyula Faculty of Education,
University of Szeged,
Hattyas utca 10, H-6725 Szeged,
Hungary.
E-mail: korus.peter@szte.hu

65 Manor Road, Desford, LE9 9JQ,
United Kingdom.
E-mail: tigris35711@gmail.com

Abstract:

The well-known Jensen inequality and Hermite--Hadamard inequality were extended using iterated integrals by Z. Retkes in 2008 and then by P. Kórus in 2019. In this paper, we consider analytical convex (concave) functions in order to obtain new refinements of Jensen's inequality. We apply the main result to the classical HM--GM--AM, AM--RMS, triangle inequalities and present an application to the geometric series. We also give Mercer type variants of Jensen's inequality.

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