Konveks Fonksiyonlarla İlgili Bazı Yeni İntegral Eşitsizlikler

Year 2018, Volume: 8 Issue: 3, 279 - 286, 30.09.2018

Çetin Yıldız Mustafa Gürbüz

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.

Keywords

konvekslik , integral eşitsizlik , konveks fonksiyonlar

Some New Integral Inequalities Related to Convex Functions

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.

Keywords

convexity , convex functions , integral inequality

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.