Araştırma Makalesi
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Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions

Yıl 2017, Cilt: 5 Sayı: 2, 180 - 185, 30.03.2017

Imdat Iscan , Huriye Kadakal Mahir Kadakal

Öz

In this paper, by using an integral identity together with both the H¨older and the Power-Mean integral inequality we established some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions.

Anahtar Kelimeler

Convex function (a m)-convex function

Kaynakça

  • S.P. Bai, S.H. Wang and F. Qi, “Some Hermite-Hadamard type inequalities for n-time differentiable (a,m)-convex functions”, Jour. of Ineq. and Appl., 2012, 2012:267.
  • M. K. Bakula, M. E. ¨Ozdemir and J. Pecaric, “Hadamard type inequalities for m-convex and (a, m)-convex functions”, J. Inequal. Pure & Appl. Math., 9(2008), Article 96, [http://jipam.vu.edu.au].
  • P. Cerone, S.S. Dragomir and J. Roumeliotis, “Some Ostrowski type inequalities for n-time differentiable mappings and applications”, Demonstratio Math., 32 (4) (1999), 697–712.
  • P. Cerone, S.S. Dragomir, J. Roumeliotis and J. Sunde, “A new generalization of the trapezoid formula for n-time differentiable mappings and applications”, Demonstratio Math., 33 (4) (2000), 719–736.
  • S.S. Dragomir and C.E.M. Pearce, “Selected Topics on Hermite-Hadamard Inequalities and Applications”, RGMIA Monographs, Victoria University, 2000, online: http://www.staxo.vu.edu.au/RGMIA/monographs/hermitehadamard.html.
  • D.Y. Hwang, “Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335–343.
  • I. Iscan, “Ostrowski type inequalities for p-convex functions”, New Trends in Mathematical Sciences, 4 (3) (2016), 140-150.
  • I. Iscan and S. Turhan, “Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral”, Moroccan J. Pure and Appl. Anal.(MJPAA), Volume 2(1) (2016), 34-46.
  • I. Iscan, “Hermite-Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935–942.
  • I. Iscan, A new generalization of some integral inequalities for (a,m)-convex functions, Mathematical Sciences 2013, 7:22,1-8, doi:10.1186/2251-7456-7-22.
  • I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are (a,m)-convex, International Journal of Engineering and Applied sciences (EAAS), 2 (3) (2013), 69-78.
  • I. Iscan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, International Journal of Pure and Applied Mathematics, 86 (4) (2013), 727-746.
  • I. Iscan, New estimates on generalization of some integral inequalities for (a,m)-convex functions, Contemporary Analysis and Applied Mathematics, Vol. 1, No. 2 (2013), 253-264.
  • M. Kadakal, H. Kadakaland, I. Iscan, “Some New Integral Inequalities for n- Times Differentiable s-Convex Functions in the First Sense”, Turkish Journal of Analysis and Number Theory, 2017, (Accepted).
  • M. Klaricic, Bakula, J. Pecaric, and M. Ribicic, “Companion inequalities to Jensen’s inequality for m-convex and (a, m)-convex functions”, J. Inequal. Pure & Appl. Math., 7(2006), Article 194.
  • S. Maden, H. Kadakal, M. Kadakal and I. Iscan, “Some new integral inequalities for n-times differentiable convex and concave functions”. Available online at: https://www.researchgate.net/publication/312529563.
  • V. G. Mihes¸an, “A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex”, Cluj-Napoca (Romania) (1993).
  • G. Toader, “Some generalizations of the convexity, Proceedings of The Colloquium On Approximation and Optimization”, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • S.H. Wang, B. Y. Xi and F. Qi, “Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex”, Analysis (Munich), 32 (2012), 247–262.
  • C¸ . Yıldız, “New inequalities of the Hermite-Hadamard type for n-time differentiable functions which are quasiconvex”, Journal of Mathematical Inequalities, 10, 3(2016), 703-711.

Yıl 2017, Cilt: 5 Sayı: 2, 180 - 185, 30.03.2017

Imdat Iscan , Huriye Kadakal Mahir Kadakal

Öz

Kaynakça

  • S.P. Bai, S.H. Wang and F. Qi, “Some Hermite-Hadamard type inequalities for n-time differentiable (a,m)-convex functions”, Jour. of Ineq. and Appl., 2012, 2012:267.
  • M. K. Bakula, M. E. ¨Ozdemir and J. Pecaric, “Hadamard type inequalities for m-convex and (a, m)-convex functions”, J. Inequal. Pure & Appl. Math., 9(2008), Article 96, [http://jipam.vu.edu.au].
  • P. Cerone, S.S. Dragomir and J. Roumeliotis, “Some Ostrowski type inequalities for n-time differentiable mappings and applications”, Demonstratio Math., 32 (4) (1999), 697–712.
  • P. Cerone, S.S. Dragomir, J. Roumeliotis and J. Sunde, “A new generalization of the trapezoid formula for n-time differentiable mappings and applications”, Demonstratio Math., 33 (4) (2000), 719–736.
  • S.S. Dragomir and C.E.M. Pearce, “Selected Topics on Hermite-Hadamard Inequalities and Applications”, RGMIA Monographs, Victoria University, 2000, online: http://www.staxo.vu.edu.au/RGMIA/monographs/hermitehadamard.html.
  • D.Y. Hwang, “Some Inequalities for n-time Differentiable Mappings and Applications”, Kyung. Math. Jour., 43 (2003), 335–343.
  • I. Iscan, “Ostrowski type inequalities for p-convex functions”, New Trends in Mathematical Sciences, 4 (3) (2016), 140-150.
  • I. Iscan and S. Turhan, “Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral”, Moroccan J. Pure and Appl. Anal.(MJPAA), Volume 2(1) (2016), 34-46.
  • I. Iscan, “Hermite-Hadamard type inequalities for harmonically convex functions”, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935–942.
  • I. Iscan, A new generalization of some integral inequalities for (a,m)-convex functions, Mathematical Sciences 2013, 7:22,1-8, doi:10.1186/2251-7456-7-22.
  • I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are (a,m)-convex, International Journal of Engineering and Applied sciences (EAAS), 2 (3) (2013), 69-78.
  • I. Iscan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, International Journal of Pure and Applied Mathematics, 86 (4) (2013), 727-746.
  • I. Iscan, New estimates on generalization of some integral inequalities for (a,m)-convex functions, Contemporary Analysis and Applied Mathematics, Vol. 1, No. 2 (2013), 253-264.
  • M. Kadakal, H. Kadakaland, I. Iscan, “Some New Integral Inequalities for n- Times Differentiable s-Convex Functions in the First Sense”, Turkish Journal of Analysis and Number Theory, 2017, (Accepted).
  • M. Klaricic, Bakula, J. Pecaric, and M. Ribicic, “Companion inequalities to Jensen’s inequality for m-convex and (a, m)-convex functions”, J. Inequal. Pure & Appl. Math., 7(2006), Article 194.
  • S. Maden, H. Kadakal, M. Kadakal and I. Iscan, “Some new integral inequalities for n-times differentiable convex and concave functions”. Available online at: https://www.researchgate.net/publication/312529563.
  • V. G. Mihes¸an, “A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex”, Cluj-Napoca (Romania) (1993).
  • G. Toader, “Some generalizations of the convexity, Proceedings of The Colloquium On Approximation and Optimization”, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.
  • S.H. Wang, B. Y. Xi and F. Qi, “Some new inequalities of Hermite-Hadamard type for n-time differentiable functions which are m-convex”, Analysis (Munich), 32 (2012), 247–262.
  • C¸ . Yıldız, “New inequalities of the Hermite-Hadamard type for n-time differentiable functions which are quasiconvex”, Journal of Mathematical Inequalities, 10, 3(2016), 703-711.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Imdat Iscan

Huriye Kadakal Bu kişi benim

Mahir Kadakal Bu kişi benim

Yayımlanma Tarihi 30 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Iscan, I., Kadakal, H., & Kadakal, M. (2017). Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences, 5(2), 180-185.
AMA Iscan I, Kadakal H, Kadakal M. Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences. Mart 2017;5(2):180-185.
Chicago Iscan, Imdat, Huriye Kadakal, ve Mahir Kadakal. “Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions”. New Trends in Mathematical Sciences 5, sy. 2 (Mart 2017): 180-85.
EndNote Iscan I, Kadakal H, Kadakal M (01 Mart 2017) Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences 5 2 180–185.
IEEE I. Iscan, H. Kadakal, ve M. Kadakal, “Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions”, New Trends in Mathematical Sciences, c. 5, sy. 2, ss. 180–185, 2017.
ISNAD Iscan, Imdat vd. “Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions”. New Trends in Mathematical Sciences 5/2 (Mart2017), 180-185.
JAMA Iscan I, Kadakal H, Kadakal M. Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences. 2017;5:180–185.
MLA Iscan, Imdat vd. “Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions”. New Trends in Mathematical Sciences, c. 5, sy. 2, 2017, ss. 180-5.
Vancouver Iscan I, Kadakal H, Kadakal M. Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions. New Trends in Mathematical Sciences. 2017;5(2):180-5.