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Year 2018, Volume: 3 Issue: 1, 14 - 31, 31.12.2018

Nurullah Kılıç Ahmet Ocak Akdemir

Abstract

References

  • M. Avcı-Ardıç, A.O.Akdemir, E.Set, New Ostrowski Like Inequalities for GG−Convex and GA−Convex Functions, Mathematical Inequalities and Applications, Volume 19, Number 4 (2016), 1159–1168.
  • G.D. Anderson , M.K. Vamanamurthy , M. Vuorinen , Generalized convexity and inequalities J. Math. Anal. Appl. 335 (2007) 1294–1308.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935-942.
  • T-Y. Zhang, A-P. Ji and F. Qi, Sone inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Le Matematiche, Vol. LXVIII (2013) Fasc. I, pp. 229239, doi: 10.4418/2013.68.1.17.
  • X-M. Zhang, Y-M. Chu, and X-H. Zhang, The Hermite-Hadamard type inequality of GA-convex functions and its application, Journal of Inequalities and Applications, Volume 2010, Article ID 507560, 11 pages, doi:10.1155/2010/507560.

Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions

Year 2018, Volume: 3 Issue: 1, 14 - 31, 31.12.2018

Nurullah Kılıç Ahmet Ocak Akdemir

Abstract

In this study, firstly two integral identity have been obtained and some Hadamard type integral inequalities have been proved for geometrically convex functions by using these two integral identities. Also, some applications related to findings have been given.


Bu çalışmada öncelikle iki integral eşitsizliği elde edilmiş ve bu iki eşitlik yardımıyla türevlenebilen geometrik konveks fonksiyonlar için bazı Hadamard tipli integral eşitsizlikler ispat edilmiştir. Ayrıca elde edilen bulgulara ait bazı uygulamalar verilmiştir. 

Keywords

Hadamard Inequality Geometrically convexity Hölder inequality

References

  • M. Avcı-Ardıç, A.O.Akdemir, E.Set, New Ostrowski Like Inequalities for GG−Convex and GA−Convex Functions, Mathematical Inequalities and Applications, Volume 19, Number 4 (2016), 1159–1168.
  • G.D. Anderson , M.K. Vamanamurthy , M. Vuorinen , Generalized convexity and inequalities J. Math. Anal. Appl. 335 (2007) 1294–1308.
  • İ. İşcan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6) (2014), 935-942.
  • T-Y. Zhang, A-P. Ji and F. Qi, Sone inequalities of Hermite-Hadamard type for GA-convex functions with applications to means, Le Matematiche, Vol. LXVIII (2013) Fasc. I, pp. 229239, doi: 10.4418/2013.68.1.17.
  • X-M. Zhang, Y-M. Chu, and X-H. Zhang, The Hermite-Hadamard type inequality of GA-convex functions and its application, Journal of Inequalities and Applications, Volume 2010, Article ID 507560, 11 pages, doi:10.1155/2010/507560.
There are 5 citations in total.

Details

Primary Language English
Journal Section Volume III, Issue I, 2018
Authors

Nurullah Kılıç This is me

Ahmet Ocak Akdemir

Publication Date December 31, 2018
Published in Issue Year 2018 Volume: 3 Issue: 1

Cite

APA Kılıç, N., & Akdemir, A. O. (2018). Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions. Turkish Journal of Science, 3(1), 14-31.
AMA Kılıç N, Akdemir AO. Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions. TJOS. December 2018;3(1):14-31.
Chicago Kılıç, Nurullah, and Ahmet Ocak Akdemir. “Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions”. Turkish Journal of Science 3, no. 1 (December 2018): 14-31.
EndNote Kılıç N, Akdemir AO (December 1, 2018) Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions. Turkish Journal of Science 3 1 14–31.
IEEE N. Kılıç and A. O. Akdemir, “Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions”, TJOS, vol. 3, no. 1, pp. 14–31, 2018.
ISNAD Kılıç, Nurullah - Akdemir, Ahmet Ocak. “Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions”. Turkish Journal of Science 3/1 (December 2018), 14-31.
JAMA Kılıç N, Akdemir AO. Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions. TJOS. 2018;3:14–31.
MLA Kılıç, Nurullah and Ahmet Ocak Akdemir. “Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions”. Turkish Journal of Science, vol. 3, no. 1, 2018, pp. 14-31.
Vancouver Kılıç N, Akdemir AO. Hadamard Type Integral Inequalities for Differentiable Geometrically Convex Functions. TJOS. 2018;3(1):14-31.
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