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Konveks Fonksiyonlarla İlgili Bazı Yeni İntegral Eşitsizlikler

Year 2018, Volume: 8 Issue: 3, 279 - 286, 30.09.2018
https://doi.org/10.21597/jist.458656

Abstract

Konveks fonksiyonları kullanarak, bir çekirdek yardımıyla bazı yeni integral eşitsizlikler elde ettik.
İspatlarda kullanılan analiz oldukça elementer olup Hölder ve Power mean eşitsizliği üzerine kurgulandı.

References

  • Alomari MW, Latif MA, Hussain S, 2012. On Ostrowski-type inequalities for functions whose derivatives are m-convex and (α,m)-convex functions with applications. Tamkang Journal of Mathematics, 43 (4): 521-532.
  • Bakula MK, Özdemir ME, Pečarič J, 2008. Hadamard Type Inequalities for m-and (α,m)-Convex Functions. Jour. of Ineq. In Pure and App. Math., Vol. 9 (4), Art. 96, 12 pp.
  • Chaudhry MA, Qadir A, Rafique M, Zubair SM, 1997. Extension of Euler's beta function. Jour. of Comp. and App. Math., Vol 78, 19-32 pp.
  • Dragomir SS, Pearce CEM, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • Gürbüz, M., 2013. Farklı Türden Konveks Fonksiyonların Çarpımı Üzerine İntegral Eşitsizlikleri ve Uygulamaları. Doktora Tezi, Fen Bilimleri Enstitüsü, Atatürk Üniversitesi, Erzurum.
  • İşcan İ, 2013. A new generalization of some integral inequalities for (α,m)-convex functions. Mathematical Sciences, 7 (22), 8 pp.
  • Lara T, Quintero Roy, Rosales E, 2017. m-Convexity and Functional Equations. Moroccan J. Pure and Appl. Anal., Vol 3(1), 56-62 pp.
  • Miheşan VG, 1993. A generalization of the convexity. Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, Romania.
  • Özdemir ME, Kavurmacı H, Set E, 2010. Ostrowski’s Type Inequalities for (α,m)-Convex Functions. Kyungpook Math. J. 50: 371-378.
  • Özdemir ME, Avcı M, Kavurmacı H, 2011. Hermite-Hadamard-type inequalities via (α,m)-convexity. Comput. Math. Appl., 61: 2614-2620.
  • Set E, Özdemir ME, Sarıkaya MZ, Karakoç F, 2017. Hermite-Hadamard type inequalities for (α,m)-convex functions via fractional integrals, Moroccan Journal of Pure and Applied Analysis 3 (1): 15-21.
  • Toader G, 1984. Some generalizations of the convexity. Proceedings of The Colloquium On Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 329-338.
  • Yıldız Ç, Gürbüz M, Akdemir AO, 2013. The Hadamard Type Inequalities for m-Convex Functions. Konuralp Journal of Mathematics, 1 (1): 40–47.
  • Yıldız Ç, 2018. New general integral inequalities for quasi-convex functions. New Trends in Mathematical Sciences, 6 (1): 1-7.

Some New Integral Inequalities Related to Convex Functions

Year 2018, Volume: 8 Issue: 3, 279 - 286, 30.09.2018
https://doi.org/10.21597/jist.458656

Abstract

We gathered several new integral inequalities with the help of a kernel and using functions which are

convex. The proofs are made with quite basic analysis and stated on Hölder and Power mean inequalities.

References

  • Alomari MW, Latif MA, Hussain S, 2012. On Ostrowski-type inequalities for functions whose derivatives are m-convex and (α,m)-convex functions with applications. Tamkang Journal of Mathematics, 43 (4): 521-532.
  • Bakula MK, Özdemir ME, Pečarič J, 2008. Hadamard Type Inequalities for m-and (α,m)-Convex Functions. Jour. of Ineq. In Pure and App. Math., Vol. 9 (4), Art. 96, 12 pp.
  • Chaudhry MA, Qadir A, Rafique M, Zubair SM, 1997. Extension of Euler's beta function. Jour. of Comp. and App. Math., Vol 78, 19-32 pp.
  • Dragomir SS, Pearce CEM, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • Gürbüz, M., 2013. Farklı Türden Konveks Fonksiyonların Çarpımı Üzerine İntegral Eşitsizlikleri ve Uygulamaları. Doktora Tezi, Fen Bilimleri Enstitüsü, Atatürk Üniversitesi, Erzurum.
  • İşcan İ, 2013. A new generalization of some integral inequalities for (α,m)-convex functions. Mathematical Sciences, 7 (22), 8 pp.
  • Lara T, Quintero Roy, Rosales E, 2017. m-Convexity and Functional Equations. Moroccan J. Pure and Appl. Anal., Vol 3(1), 56-62 pp.
  • Miheşan VG, 1993. A generalization of the convexity. Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca, Romania.
  • Özdemir ME, Kavurmacı H, Set E, 2010. Ostrowski’s Type Inequalities for (α,m)-Convex Functions. Kyungpook Math. J. 50: 371-378.
  • Özdemir ME, Avcı M, Kavurmacı H, 2011. Hermite-Hadamard-type inequalities via (α,m)-convexity. Comput. Math. Appl., 61: 2614-2620.
  • Set E, Özdemir ME, Sarıkaya MZ, Karakoç F, 2017. Hermite-Hadamard type inequalities for (α,m)-convex functions via fractional integrals, Moroccan Journal of Pure and Applied Analysis 3 (1): 15-21.
  • Toader G, 1984. Some generalizations of the convexity. Proceedings of The Colloquium On Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 329-338.
  • Yıldız Ç, Gürbüz M, Akdemir AO, 2013. The Hadamard Type Inequalities for m-Convex Functions. Konuralp Journal of Mathematics, 1 (1): 40–47.
  • Yıldız Ç, 2018. New general integral inequalities for quasi-convex functions. New Trends in Mathematical Sciences, 6 (1): 1-7.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Çetin Yıldız This is me 0000-0002-8302-343X

Mustafa Gürbüz 0000-0002-7092-4298

Publication Date September 30, 2018
Submission Date February 10, 2018
Acceptance Date April 9, 2018
Published in Issue Year 2018 Volume: 8 Issue: 3

Cite

APA Yıldız, Ç., & Gürbüz, M. (2018). Some New Integral Inequalities Related to Convex Functions. Journal of the Institute of Science and Technology, 8(3), 279-286. https://doi.org/10.21597/jist.458656
AMA Yıldız Ç, Gürbüz M. Some New Integral Inequalities Related to Convex Functions. J. Inst. Sci. and Tech. September 2018;8(3):279-286. doi:10.21597/jist.458656
Chicago Yıldız, Çetin, and Mustafa Gürbüz. “Some New Integral Inequalities Related to Convex Functions”. Journal of the Institute of Science and Technology 8, no. 3 (September 2018): 279-86. https://doi.org/10.21597/jist.458656.
EndNote Yıldız Ç, Gürbüz M (September 1, 2018) Some New Integral Inequalities Related to Convex Functions. Journal of the Institute of Science and Technology 8 3 279–286.
IEEE Ç. Yıldız and M. Gürbüz, “Some New Integral Inequalities Related to Convex Functions”, J. Inst. Sci. and Tech., vol. 8, no. 3, pp. 279–286, 2018, doi: 10.21597/jist.458656.
ISNAD Yıldız, Çetin - Gürbüz, Mustafa. “Some New Integral Inequalities Related to Convex Functions”. Journal of the Institute of Science and Technology 8/3 (September 2018), 279-286. https://doi.org/10.21597/jist.458656.
JAMA Yıldız Ç, Gürbüz M. Some New Integral Inequalities Related to Convex Functions. J. Inst. Sci. and Tech. 2018;8:279–286.
MLA Yıldız, Çetin and Mustafa Gürbüz. “Some New Integral Inequalities Related to Convex Functions”. Journal of the Institute of Science and Technology, vol. 8, no. 3, 2018, pp. 279-86, doi:10.21597/jist.458656.
Vancouver Yıldız Ç, Gürbüz M. Some New Integral Inequalities Related to Convex Functions. J. Inst. Sci. and Tech. 2018;8(3):279-86.