BibTex RIS Kaynak Göster

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Yıl 2014, Cilt: 1 Sayı: 2, 53 - 61, 01.12.2014

Öz

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

Kaynakça

  • B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. Vol. 7. 1966.
  • J. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
  • S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • R.B. Manfrino, R.V. Delgado, J.A.G. Ortega, Inequalities a Mathematical Olympiad Approach, Birkhauser, 2009.
  • D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers,Dordrecht, 1993.
  • J.E. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991.
  • D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
  • A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Mathematicae 44 (1992) 249-258.
  • A. Skowronski, On wright-convex stochastic processes, Annales Mathematicae Silesianne 9 (1995) 29
  • S.S. Dragomir and B. Mond, Integral inequalities of Hadamard’s type for log-convex functions, Demonstratio Math., 31 (2) (1998), 354-364.
  • S. S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, The Australian Math. Soc. Gazette, 28.3 (2001): 129-133
  • M. Tunç, Some integral inequalities for logarithmically convex functions, Journal of the Egyptian Mathematical Society, Volume 22 (2014), 177-181
  • K. Nikodem, On convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
  • S.S. Dragomir, J.E. Pecaric, J. Sandor, A note on the Jensen–Hadamard inequality, Anal. Num. Theor. Approx. 19 (1990) 29–34.
  • 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.
  • S.S. Dragomir, B. Mond, Integral inequalities of Hadamard type for log-convex functions, Demonstratio Math. 31 (2) (1998) 354–364.
  • B.G. Pachpatte, A note on integral inequalities involving two log-convex functions, Math. Ineq. Appl. 7 (4) (2004) 511–515.
  • S.S. Dragomir, Two functions in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992) 49–
  • S.S. Dragomir, Some remarks on Hadamard’s inequalities for convex functions, Extracta Math. 9 (2) (1994) 88–94.
  • S.S. Dragomir, Refinements of the Hermite–Hadamard integral inequality for log-convex functions, RGMIA Res. Rep. Collect. 3 (4) (2000) 527–533.
  • M.E. Özdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Lett. 13 (2000) 19–25.
  • N. O. Bekar, H. G. Akdemir and İ. İşcan, On Strongly GA-convex functions and stochastic processes, AIP Conference Proceedings 1611, 363 (2014).
  • 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.
  • M. Z. Sarikaya and H. Yildiz, On Hermite-Hadamard-type inequalities strongly log-convex functions, submitted.

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

Yıl 2014, Cilt: 1 Sayı: 2, 53 - 61, 01.12.2014

Öz

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

Kaynakça

  • B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. Vol. 7. 1966.
  • J. Pecaric, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
  • S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • R.B. Manfrino, R.V. Delgado, J.A.G. Ortega, Inequalities a Mathematical Olympiad Approach, Birkhauser, 2009.
  • D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers,Dordrecht, 1993.
  • J.E. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, 1991.
  • D. Kotrys, Hermite-hadamart inequality for convex stochastic processes, Aequationes Mathematicae 83 (2012) 143-151.
  • A. Skowronski, On some properties of J-convex stochastic processes, Aequationes Mathematicae 44 (1992) 249-258.
  • A. Skowronski, On wright-convex stochastic processes, Annales Mathematicae Silesianne 9 (1995) 29
  • S.S. Dragomir and B. Mond, Integral inequalities of Hadamard’s type for log-convex functions, Demonstratio Math., 31 (2) (1998), 354-364.
  • S. S. Dragomir, Refinements of the Hermite-Hadamard integral inequality for log-convex functions, The Australian Math. Soc. Gazette, 28.3 (2001): 129-133
  • M. Tunç, Some integral inequalities for logarithmically convex functions, Journal of the Egyptian Mathematical Society, Volume 22 (2014), 177-181
  • K. Nikodem, On convex stochastic processes, Aequationes Mathematicae 20 (1980) 184-197.
  • S.S. Dragomir, J.E. Pecaric, J. Sandor, A note on the Jensen–Hadamard inequality, Anal. Num. Theor. Approx. 19 (1990) 29–34.
  • 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.
  • S.S. Dragomir, B. Mond, Integral inequalities of Hadamard type for log-convex functions, Demonstratio Math. 31 (2) (1998) 354–364.
  • B.G. Pachpatte, A note on integral inequalities involving two log-convex functions, Math. Ineq. Appl. 7 (4) (2004) 511–515.
  • S.S. Dragomir, Two functions in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992) 49–
  • S.S. Dragomir, Some remarks on Hadamard’s inequalities for convex functions, Extracta Math. 9 (2) (1994) 88–94.
  • S.S. Dragomir, Refinements of the Hermite–Hadamard integral inequality for log-convex functions, RGMIA Res. Rep. Collect. 3 (4) (2000) 527–533.
  • M.E. Özdemir, A theorem on mappings with bounded derivatives with applications to quadrature rules and means, Appl. Math. Lett. 13 (2000) 19–25.
  • N. O. Bekar, H. G. Akdemir and İ. İşcan, On Strongly GA-convex functions and stochastic processes, AIP Conference Proceedings 1611, 363 (2014).
  • 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.
  • M. Z. Sarikaya and H. Yildiz, On Hermite-Hadamard-type inequalities strongly log-convex functions, submitted.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Muharrem Tomar Bu kişi benim

Erhan Set Bu kişi benim

Nurgül Okur Bekar Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 1 Sayı: 2

Kaynak Göster

APA Tomar, M., Set, E., & Bekar, N. O. (2014). On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes. Küresel Mühendislik Çalışmaları Dergisi, 1(2), 53-61.
AMA Tomar M, Set E, Bekar NO. On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes. Küresel Mühendislik Çalışmaları Dergisi. Aralık 2014;1(2):53-61.
Chicago Tomar, Muharrem, Erhan Set, ve Nurgül Okur Bekar. “On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes”. Küresel Mühendislik Çalışmaları Dergisi 1, sy. 2 (Aralık 2014): 53-61.
EndNote Tomar M, Set E, Bekar NO (01 Aralık 2014) On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes. Küresel Mühendislik Çalışmaları Dergisi 1 2 53–61.
IEEE M. Tomar, E. Set, ve N. O. Bekar, “On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes”, Küresel Mühendislik Çalışmaları Dergisi, c. 1, sy. 2, ss. 53–61, 2014.
ISNAD Tomar, Muharrem vd. “On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes”. Küresel Mühendislik Çalışmaları Dergisi 1/2 (Aralık 2014), 53-61.
JAMA Tomar M, Set E, Bekar NO. On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes. Küresel Mühendislik Çalışmaları Dergisi. 2014;1:53–61.
MLA Tomar, Muharrem vd. “On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes”. Küresel Mühendislik Çalışmaları Dergisi, c. 1, sy. 2, 2014, ss. 53-61.
Vancouver Tomar M, Set E, Bekar NO. On Hermite-Hadamard-Type Inequalities for Strongly-Log Convex Stochastic Processes. Küresel Mühendislik Çalışmaları Dergisi. 2014;1(2):53-61.