Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2018, 6(1), 9-15
DOI: 10.12691/tjant-6-1-2
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Obtaining of Some New Inequalities Using Functıonals for GA-Convex Functions

İmdat İşcan1, Mahir Kadakal1, and Yasemin Külekçi2

1Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, TÜRKİYE

2Institute of Sciences and Arts, Giresun University, Giresun, TÜRKİYE

Pub. Date: February 27, 2018

Cite this paper:
İmdat İşcan, Mahir Kadakal and Yasemin Külekçi. Obtaining of Some New Inequalities Using Functıonals for GA-Convex Functions. Turkish Journal of Analysis and Number Theory. 2018; 6(1):9-15. doi: 10.12691/tjant-6-1-2


In this paper, we get the fractional integral inequalities obtained for geometric arithmetically (GA) convex functions by using functionals. The left hand side of the Hermite-Hadamard and Hermite-Hadamard-Fejér inequalities obtained by using Hadamard fractional integrals for Geometric Arithmetically-convex functions was obtained via functionals. We conclude that some results obtained in this paper are the refinements of the earlier results.

convex function integral inequalities GA-Convex function functionals Riemann-Liouville fractional integrals Hadamard fractional integrals

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[1]  M. Bessenyei and Z. Páles, Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl., 6 (2003), 379-392.
[2]  S.S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.
[3]  S.S. Dragomir and G.H. Toader, Some inequalities for m-convex functions, Stud. Univ. Babes-Bolyai Math., 38 (1993), 21-28.
[4]  S.S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math., 32 (1999), 687-696.
[5]  A.E. Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal., 4 (2010), 365-369.
[6]  M.Z. Sarıkaya, Aziz Sağlam and Hüseyin Yıldırım, On some Hadamard-type inequalities for h-convex functions, J. Math. Inequal., 2 (2008), 335-341.
[7]  M.Z. Sarıkaya Erhan Set, Hatice Yaldiz, Nagihan Başak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013), 2403-2407.
[8]  G.S. Yang and K.L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.
[9]  G.S. Yang and M.C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.
[10]  Niculescu CP: Convexity according to the geometric mean. Math. Inequal. Appl. 2000, 3(2):155-167. 10.7153/mia-03-19.
[11]  Ruiyin Xiang, Refinements of Hermite-Hadamard Type Inequalıtıes for Convex Functıons Via Fractıonal Integrals, J. Appl. Math. & Informatics Vol. 33(2015), No. 1-2, pp. 119-125.
[12]  Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
[13]  J. Hua, B.-Y. Xi, and F. Qi, “Hermite-Hadamard Type Inequalities for Geometric-Arithmetically s-Convex Functions”, Commun. Korean Math. Soc. 29 (2014), No. 1, pp. 51–63, 2014.
[14]  İ. İşcan, Hermite-Hadamard type inequalities for GA-s-convex functions, Le Matematiche, Vol. LXIX (2014) – Fasc. II, pp. 129-146.
[15]  İ. İşcan New general integral inequalities for quasi-geometrically convex functions via fractional integrals Journal of Inequalities and Applications 2013, 2013:491.
[16]  M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometrically-arithmetically-convex functions with applications, RGMIA Research Report Collection, 18(2015), Article 25, 18 pp.