-

Abstract

In the present the work we introduce strongly logarithmic convex stochastic processes. Also, we obtain Hermite-Hadamard type integral inequalities for these processes

Keywords

• Hermite-Hadamar’d inequalities,strongly convex with modulus c> 0,log-convex function

On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes

Öz

Bu çalışmada, güçlü logaritmik konveks stokastik süreci tanıtılmaktadır. Ayrıca, bu aüreçler için Hermite-Hadamard tipi integral eşitsizliklerini elde edilmektedir

Anahtar Kelimeler

• Hermite-Hadamard eşitsizliği, modüllü güçlü konveks, log-konveks fonksiyon, skotastik süreç

Kaynakça

1. B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. Vol. 7. 1966.
2. J. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
3. S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
4. R.B. Manfrino, R.V. Delgado, J.A.G. Ortega, Inequalities a Mathematical Olympiad Approach, Birkhauser, 2009.
5. D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers,Dordrecht, 1993.
6. J.E. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991.
7. D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
8. A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Mathematicae 44 (1992) 249-258.

9. A. Skowronski, On wright-convex stochastic processes, Annales Mathematicae Silesianne 9 (1995) 29
10. S.S. Dragomir and B. Mond, Integral inequalities of Hadamard’s type for log-convex functions, Demonstratio Math., 31 (2) (1998), 354-364.
11. S. S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, The Australian Math. Soc. Gazette, 28.3 (2001): 129-133
12. M. Tunç, Some integral inequalities for logarithmically convex functions, Journal of the Egyptian Mathematical Society, Volume 22 (2014), 177-181
13. K. Nikodem, On convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
14. S.S. Dragomir, J.E. Pecaric, J. Sandor, A note on the Jensen–Hadamard inequality, Anal. Num. Theor. Approx. 19 (1990) 29–34.
15. U.S. K rmac , M.E. Özdemir, Some inequalities for mappings whose derivatives are bounded and applications to specials means of real numbers, Appl. Math. Lett. 17 (2004) 641–645.
16. S.S. Dragomir, B. Mond, Integral inequalities of Hadamard type for log-convex functions, Demonstratio Math. 31 (2) (1998) 354–364.
17. B.G. Pachpatte, A note on integral inequalities involving two log-convex functions, Math. Ineq. Appl. 7 (4) (2004) 511–515.
18. S.S. Dragomir, Two functions in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992) 49–
19. S.S. Dragomir, Some remarks on Hadamard’s inequalities for convex functions, Extracta Math. 9 (2) (1994) 88–94.
20. S.S. Dragomir, Refinements of the Hermite–Hadamard integral inequality for log-convex functions, RGMIA Res. Rep. Collect. 3 (4) (2000) 527–533.
21. M.E. Özdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Lett. 13 (2000) 19–25.
22. N. O. Bekar, H. G. Akdemir and İ. İşcan, On Strongly GA-convex functions and stochastic processes, AIP Conference Proceedings 1611, 363 (2014).
23. M. Tomar, E. Set, and S. Maden, Hermite–Hadamard type inequalities for log-convex stochastic processes, submitted. D. Kotrys and K.Nikodem, Quasiconvex stochastic processes and a separation theorem, Aequationes Mathematicae July (2014) 1-8.
24. M. Z. Sarikaya and H. Yildiz, On Hermite-Hadamard-type inequalities strongly log-convex functions, submitted.