Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: https://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(6), 202-207
DOI: 10.12691/tjant-2-6-3
Open AccessArticle

Hermite-Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense

ERHAN SET1, MUHARREM TOMAR1, and SELAHATTIN MADEN1

1Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey

Pub. Date: November 23, 2014

Cite this paper:
ERHAN SET, MUHARREM TOMAR and SELAHATTIN MADEN. Hermite-Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense. Turkish Journal of Analysis and Number Theory. 2014; 2(6):202-207. doi: 10.12691/tjant-2-6-3

Abstract

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

Keywords:
Hermite Hadamard Inequality s-convex functions convex stochastic process s-convex stochastic process

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References:

[1]  K. Nikodem, on convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
 
[2]  A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Mathematicae 44 (1992) 249-258.
 
[3]  A. Skowronski, On wright-convex stochastic processes, Annales Mathematicae Silesianne 9(1995) 29-32.
 
[4]  D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
 
[5]  S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4) (1999), 687-696.
 
[6]  H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Mathematicae, 48 (1994), 100-111.
 
[7]  S. Maden, M. Tomar and E. Set, s-convex stochastic processes in the first sense, Pure and Applied Mathematics Letters, in press.
 
[8]  D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.