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

Year 2017, Volume: 5 Issue: 2, 180 - 185, 30.03.2017

Imdat Iscan , Huriye Kadakal Mahir Kadakal

Abstract

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.

Keywords

Convex function (a m)-convex function

References

  • 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.

Year 2017, Volume: 5 Issue: 2, 180 - 185, 30.03.2017

Imdat Iscan , Huriye Kadakal Mahir Kadakal

Abstract

References

  • 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.
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Imdat Iscan

Huriye Kadakal This is me

Mahir Kadakal This is me

Publication Date March 30, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

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. March 2017;5(2):180-185.
Chicago Iscan, Imdat, Huriye Kadakal, and 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, no. 2 (March 2017): 180-85.
EndNote Iscan I, Kadakal H, Kadakal M (March 1, 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, and M. Kadakal, “Some new integral inequalities for functions whose nth derivatives in absolute value are (a,m)-convex functions”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 180–185, 2017.
ISNAD Iscan, Imdat et al. “Some New Integral Inequalities for Functions Whose Nth Derivatives in Absolute Value Are (a,m)-Convex Functions”. New Trends in Mathematical Sciences 5/2 (March 2017), 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 et al. “Some New Integral Inequalities for Functions Whose Nth Derivatives in Absolute Value Are (a,m)-Convex Functions”. New Trends in Mathematical Sciences, vol. 5, no. 2, 2017, pp. 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.
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