Ohlin and Levin–Stečkin-Type Results for Strongly Convex Functions-Reference-Cited by-同舟云学术

Ohlin and Levin–Stečkin-Type Results for Strongly Convex Functions

Published:2020-07-01 Issue:1 Volume:34 Page:123-132
ISSN:2391-4238
Container-title:Annales Mathematicae Silesianae
language:en
Short-container-title:

Author:

Nikodem Kazimierz¹,Rajba Teresa¹

Affiliation:

1. University of Bielsko-Biala , Department of Mathematics , Willowa 2, 43-309 Bielsko-Biała , Poland

Abstract

Abstract Counterparts of the Ohlin and Levin–Stečkin theorems for strongly convex functions are proved. An application of these results to obtain some known inequalities related with strongly convex functions in an alternative and unified way is presented.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/amsil-2020-0017

Reference18 articles.

1. [1] M. Denuit, C. Lefevre, and M. Shaked, The s-convex orders among real random variables, with applications, Math. Inequal. Appl. 1 (1998), 585–613.

2. [2] J.-B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis, Springer– Verlag, Berlin–Heidelberg, 2001.10.1007/978-3-642-56468-0

3. [3] M. Klaričić Bakula and K. Nikodem, On the converse Jensen inequality for strongly convex functions, J. Math. Anal. Appl. 434 (2016), 516–522.10.1016/j.jmaa.2015.09.032

4. [4] V.I. Levin and S.B. Stečkin, Inequalities, Amer. Math. Soc. Transl. (2) 14 (1960), 1–29.

5. [5] N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193–199.10.1007/s00010-010-0043-0

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