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Year 2016, Volume: 4 Issue: 3, 140 - 150, 30.09.2016

İmdat Iscan

Abstract

References

  • J. Aczél, A generalization of the notion of convex functions, Norske Vid. Selsk. Forhd., Trondhjem 19(24) (1947), 87–90.
  • M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
  • M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Applied Mathematics Letters 23(9) (2010), 1071-1076.
  • G. Aumann, Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten, Bayer. Akad. Wiss.Math.-Natur. Kl. Abh., Math. Ann. 109 (1933), 405–413.
  • I. A. Baloch and İ. İşcan, Some Ostrowski Type Inequalities For Harmonically (s,m)- convex functoins in Second Sense, International Journal of Analysis, vol. 2015 (2015), Article ID 672675, 9 pages, http://dx.doi.org/10.1155/2015/672675.
  • P. Cerone and S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Mathematica, Warsaw Technical University Institute of Mathematics 37(2) (2004), 299-308.
  • Z. B. Fang, R. Shi, On the (p,h)-convex function and some integral inequalities, J. Inequal. Appl. 2014(45) (2014), 16 pages.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions. Hacet. J. Math. Stat. 43(6) (2014), 935–942.
  • İ. İşcan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp journal of Mathematics, 3(1)(2015), 63-74.
  • İ. İşcan, Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian Mathematical Society 40(2) (2014), 373-386.
  • İ. İşcan, S. Numan, Ostrowski type inequalities for harmonically quasi-convex functions, Electronic Journal of Mathematical Analysis and Applications 2(2) (2014), 189-198.
  • J. Matkowski, Convex functions with respect to a mean and a characterization of quasi-arithmetic means, Real Anal. Exchange 29 (2003/2004), 229–246.
  • M. V. Mihai, M. A. Noor, K. I. Noor and M. U. Awan, New estimates for trapezoidal like inequalities via differentiable (p,h)-convex functions, Researchgate doi: 10.13140/RG.2.1.5106.5046. Available online at https://www.researchgate.net/publication/282912293.
  • C. P. Niculescu, "Convexity according to the geometric mean", Math. Inequal. Appl. 3(2) (2000), 155-167.
  • C.P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (2003) 571–579.
  • M. A. Noor, K. I. Noor, M. V. Mihai, and M. U. Awan, Hermite-Hadamard inequalities for differentiable p-convex functions using hypergeometric functions, Researchgate doi: 10.13140/RG.2.1.2485.0648. Available online at https://www.researchgate.net/publication/282912282.
  • M. A. Noor, K. I. Noor, S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab University Journal of Mathematics, 47(2) (2015), 19-27.
  • A. Ostrowski, Über die Absolutabweichung einer differentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
  • K. S. Zhang, J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007), 130-133.

Ostrowski type inequalities for p-convex functions

Year 2016, Volume: 4 Issue: 3, 140 - 150, 30.09.2016

İmdat Iscan

Abstract




In this paper, we give a different version of the
concept of -convex functions and obtain some new properties of -convex functions. Moreover we establish some Ostrowski type inequalities
for the class of functions whose derivatives in absolute values at certain
powers are -convex.




Keywords

p-convex function Ostrowski type inequality

References

  • J. Aczél, A generalization of the notion of convex functions, Norske Vid. Selsk. Forhd., Trondhjem 19(24) (1947), 87–90.
  • M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965.
  • M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Applied Mathematics Letters 23(9) (2010), 1071-1076.
  • G. Aumann, Konvexe Funktionen und Induktion bei Ungleichungen zwischen Mittelverten, Bayer. Akad. Wiss.Math.-Natur. Kl. Abh., Math. Ann. 109 (1933), 405–413.
  • I. A. Baloch and İ. İşcan, Some Ostrowski Type Inequalities For Harmonically (s,m)- convex functoins in Second Sense, International Journal of Analysis, vol. 2015 (2015), Article ID 672675, 9 pages, http://dx.doi.org/10.1155/2015/672675.
  • P. Cerone and S. Dragomir, Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions, Demonstratio Mathematica, Warsaw Technical University Institute of Mathematics 37(2) (2004), 299-308.
  • Z. B. Fang, R. Shi, On the (p,h)-convex function and some integral inequalities, J. Inequal. Appl. 2014(45) (2014), 16 pages.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions. Hacet. J. Math. Stat. 43(6) (2014), 935–942.
  • İ. İşcan, Ostrowski type inequalities for harmonically s-convex functions, Konuralp journal of Mathematics, 3(1)(2015), 63-74.
  • İ. İşcan, Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian Mathematical Society 40(2) (2014), 373-386.
  • İ. İşcan, S. Numan, Ostrowski type inequalities for harmonically quasi-convex functions, Electronic Journal of Mathematical Analysis and Applications 2(2) (2014), 189-198.
  • J. Matkowski, Convex functions with respect to a mean and a characterization of quasi-arithmetic means, Real Anal. Exchange 29 (2003/2004), 229–246.
  • M. V. Mihai, M. A. Noor, K. I. Noor and M. U. Awan, New estimates for trapezoidal like inequalities via differentiable (p,h)-convex functions, Researchgate doi: 10.13140/RG.2.1.5106.5046. Available online at https://www.researchgate.net/publication/282912293.
  • C. P. Niculescu, "Convexity according to the geometric mean", Math. Inequal. Appl. 3(2) (2000), 155-167.
  • C.P. Niculescu, Convexity according to means, Math. Inequal. Appl. 6 (2003) 571–579.
  • M. A. Noor, K. I. Noor, M. V. Mihai, and M. U. Awan, Hermite-Hadamard inequalities for differentiable p-convex functions using hypergeometric functions, Researchgate doi: 10.13140/RG.2.1.2485.0648. Available online at https://www.researchgate.net/publication/282912282.
  • M. A. Noor, K. I. Noor, S. Iftikhar, Nonconvex Functions and Integral Inequalities, Punjab University Journal of Mathematics, 47(2) (2015), 19-27.
  • A. Ostrowski, Über die Absolutabweichung einer differentiebaren funktion von ihren integralmittelwert, Comment. Math. Helv., 10 (1938), 226–227.
  • K. S. Zhang, J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1) (2007), 130-133.
There are 19 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

İmdat Iscan

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Iscan, İ. (2016). Ostrowski type inequalities for p-convex functions. New Trends in Mathematical Sciences, 4(3), 140-150.
AMA Iscan İ. Ostrowski type inequalities for p-convex functions. New Trends in Mathematical Sciences. September 2016;4(3):140-150.
Chicago Iscan, İmdat. “Ostrowski Type Inequalities for P-Convex Functions”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 140-50.
EndNote Iscan İ (September 1, 2016) Ostrowski type inequalities for p-convex functions. New Trends in Mathematical Sciences 4 3 140–150.
IEEE İ. Iscan, “Ostrowski type inequalities for p-convex functions”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 140–150, 2016.
ISNAD Iscan, İmdat. “Ostrowski Type Inequalities for P-Convex Functions”. New Trends in Mathematical Sciences 4/3 (September 2016), 140-150.
JAMA Iscan İ. Ostrowski type inequalities for p-convex functions. New Trends in Mathematical Sciences. 2016;4:140–150.
MLA Iscan, İmdat. “Ostrowski Type Inequalities for P-Convex Functions”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 140-5.
Vancouver Iscan İ. Ostrowski type inequalities for p-convex functions. New Trends in Mathematical Sciences. 2016;4(3):140-5.
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