Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2019, 7(1), 23-32
DOI: 10.12691/tjant-7-1-5
Open AccessArticle

(m,r)-Convex Functions

Huriye Kadakal1,

1Ministry of Education, Bulancak Bahçelievler Anatolian High School, Giresun, Turkey

Pub. Date: February 25, 2019

Cite this paper:
Huriye Kadakal. (m,r)-Convex Functions. Turkish Journal of Analysis and Number Theory. 2019; 7(1):23-32. doi: 10.12691/tjant-7-1-5

Abstract

In this paper, we introduce a new class of extended (m,r)-convex function and we establish the Hermite-Hadamard inequality for (m,r)-convex functions. Some special cases are discussed. Results represent significant refinement and improvement of the previous results. The definition of (m,r)-convex function is given for the first time in the literature and moreover, the results obtained in special cases coincide with the well-known results in the literature.

Keywords:
convex function r-convex function m-convex function -convex Hermite-Hadamard inequality

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