TY  - JOUR
T1  - On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes
AU  - Tomar, Muharrem
AU  - Set, Erhan
AU  - Bekar, Nurgül Okur
PY  - 2014
DA  - December
JF  - Küresel Mühendislik Çalışmaları Dergisi
PB  - Veli TÜRKMENOĞLU
WT  - DergiPark
SN  - 2149-2735
SP  - 53
EP  - 61
VL  - 1
IS  - 2
LA  - tr
AB  - Bu çalışmada, güçlü logaritmik konveks stokastik süreci tanıtılmaktadır. Ayrıca, bu aüreçler için Hermite-Hadamard tipi integral eşitsizliklerini elde edilmektedir
KW  - Hermite-Hadamard eşitsizliği
KW  - modüllü güçlü konveks
KW  - log-konveks fonksiyon
KW  - skotastik süreç
N2  - In the present the work we introduce strongly logarithmic convex stochastic processes. Also, we obtain Hermite-Hadamard type integral inequalities for these processes
CR  - B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. Vol. 7. 1966.
CR  - J. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
CR  - S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
CR  - R.B. Manfrino, R.V. Delgado, J.A.G. Ortega, Inequalities a Mathematical Olympiad Approach, Birkhauser, 2009.
CR  - D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers,Dordrecht, 1993.
CR  - J.E. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991.
CR  - D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
CR  - A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Mathematicae 44 (1992) 249-258.
CR  - A. Skowronski, On wright-convex stochastic processes, Annales Mathematicae Silesianne 9 (1995) 29
CR  - S.S. Dragomir and B. Mond, Integral inequalities of Hadamard’s type for log-convex functions, Demonstratio Math., 31 (2) (1998), 354-364.
CR  - S. S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, The Australian Math. Soc. Gazette, 28.3 (2001): 129-133
CR  - M. Tunç, Some integral inequalities for logarithmically convex functions, Journal of the Egyptian Mathematical Society, Volume 22 (2014), 177-181
CR  - K. Nikodem, On convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
CR  - S.S. Dragomir, J.E. Pecaric, J. Sandor, A note on the Jensen–Hadamard inequality, Anal. Num. Theor. Approx. 19 (1990) 29–34.
CR  - 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.
CR  - S.S. Dragomir, B. Mond, Integral inequalities of Hadamard type for log-convex functions, Demonstratio Math. 31 (2) (1998) 354–364.
CR  - B.G. Pachpatte, A note on integral inequalities involving two log-convex functions, Math. Ineq. Appl. 7 (4) (2004) 511–515.
CR  - S.S. Dragomir, Two functions in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992) 49–
CR  - S.S. Dragomir, Some remarks on Hadamard’s inequalities for convex functions, Extracta Math. 9 (2) (1994) 88–94.
CR  - S.S. Dragomir, Refinements of the Hermite–Hadamard integral inequality for log-convex functions, RGMIA Res. Rep. Collect. 3 (4) (2000) 527–533.
CR  - M.E. Özdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Lett. 13 (2000) 19–25.
CR  - N. O. Bekar, H. G. Akdemir and İ. İşcan, On Strongly GA-convex functions and stochastic processes, AIP Conference Proceedings 1611, 363 (2014).
CR  - 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.
CR  - M. Z. Sarikaya and H. Yildiz, On Hermite-Hadamard-type inequalities strongly log-convex functions, submitted.
UR  - https://dergipark.org.tr/en/pub/kmcd/issue//204752
L1  - https://dergipark.org.tr/en/download/article-file/180576
ER  -