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Yang, G.S., Refinementes of Hadamard inequality for r-convex functions. Indian J. Pure Appl. Math. 32(10), 1571-1579 (2001).

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Article

(m,r)-Convex Functions

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


Turkish Journal of Analysis and Number Theory. 2019, Vol. 7 No. 1, 23-32
DOI: 10.12691/tjant-7-1-5
Copyright © 2019 Science and Education Publishing

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.

Correspondence to: Huriye  Kadakal, Ministry of Education, Bulancak Bahçelievler Anatolian High School, Giresun, Turkey. Email: huriyekadakal@hotmail.com

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