Research Article
Year 2016, Volume 4, Issue 2, 1 - 9, 15.10.2016

### References

• [1] Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
• [2] Dahmani, Z. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(2010), no. 1, 51-58.
• [3] Dragomir, S. S., Inequalities of Jensen type for '-convex functions, Fasc. Math. 55(2015), 35-52.
• [4] Hudzik H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1994), no. 1, 100-111.
• [5] Işcan, I., Bekar, K. and Numan, S., Hermite-Hadamard an Simpson type inequalities for diFFerentiable quasi-geometrically convex func- tions, Turkish J: of Anal. and Number Theory, 2(2014), no. 2, 42-46.
• [6] Işcan, I., New estimates on generalization of some integral inequalities for ds-convex functions and their applications, Int. J. Pure Appl. Math., 86(2013), no. 4, 727-746.
• [7] Işcan, I., Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute value are quasi-convex Konuralp Journal of Mathematics, 1(2013), no. 2, 67-79.
• [8] Işcan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals presented
• [9] Kavurmaci, H., Avci, M. and  Ozdemir, M. E., New inequalities of Hermite- Hadamard's type for convex functions with applications, Journ. of Inequal. and Appl., 2011:86 (2011).
• [10] Mihesan, V. G., A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex, Cluj-Napoca, Romania (1993).
• [11]  Ozdemir, M. E., Avic, M. and Kavurmaci, H., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, arXiv:1202.0380v1[math.CA].
• [12] Park, J., Some new Hermite-Hadamard-like type inequalities on geometrically convex functions, Inter. J. of Math. Anal., 8(16) (2014),793-802.
• [13] Park, J., On Some Integral Inequalities for Twice Differentiable Quasi-Convex and Convex Functions via Fractional Integrals, Applied Mathematical Sciences, Vol. 9(62) (2015), 3057-3069 HIKARI Ltd, www.m-hikari.com. http://dx.doi.org/10.12988/ams.2015.53248.
• [14] Samko, S.G., Kilbas A.A. and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, 1993, ISBN 2881248640.
• [15] Sarikaya, M. Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract and applied analysis, 2012 (2012) 10 pages.
• [16] Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N., Hermite- Hadamard's inequalities for fractional integrals and related frac- tional inequalities, Math. and Comput. Model., 2011 (2011).
• [17] Set, E., Sarikaya, M. Z. and  Ozdemir, M. E., Some Ostrowski's type Inequalities for functions whose second derivatives are s-convex in the second sense, arXiv:1006.24 88v1 [math. CA] 12 June 2010.
• [18] Set, E.,  Ozdemir, M. E., Sarikaya M. Z., Karako, F., Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals, Khayyam J. Math., 1(1) (2015) 62-70.
• [19] Toader, Gh., On a generalization of the convexity, Mathematica, 30(53) (1988), 83-87.
• [20] Tunc, M., On some new inequalities for convex functions, Turk. J. Math., 35(2011), 1-7.
• [21] Tunc, M. and Yildirim, H., On MT-Convexity, arXiv: 1205.5453 [math. CA] 24 May 2012

### SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS

Year 2016, Volume 4, Issue 2, 1 - 9, 15.10.2016

### Abstract

In this paper, we obtain new estimates on generalization of Hermite-Hadamard type inequalities for functions whose second derivatives is $\varphi -$ convex via fractional integrals.

### References

• [1] Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
• [2] Dahmani, Z. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(2010), no. 1, 51-58.
• [3] Dragomir, S. S., Inequalities of Jensen type for '-convex functions, Fasc. Math. 55(2015), 35-52.
• [4] Hudzik H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1994), no. 1, 100-111.
• [5] Işcan, I., Bekar, K. and Numan, S., Hermite-Hadamard an Simpson type inequalities for diFFerentiable quasi-geometrically convex func- tions, Turkish J: of Anal. and Number Theory, 2(2014), no. 2, 42-46.
• [6] Işcan, I., New estimates on generalization of some integral inequalities for ds-convex functions and their applications, Int. J. Pure Appl. Math., 86(2013), no. 4, 727-746.
• [7] Işcan, I., Generalization of different type integral inequalities via fractional integrals for functions whose second derivatives absolute value are quasi-convex Konuralp Journal of Mathematics, 1(2013), no. 2, 67-79.
• [8] Işcan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals presented
• [9] Kavurmaci, H., Avci, M. and  Ozdemir, M. E., New inequalities of Hermite- Hadamard's type for convex functions with applications, Journ. of Inequal. and Appl., 2011:86 (2011).
• [10] Mihesan, V. G., A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex, Cluj-Napoca, Romania (1993).
• [11]  Ozdemir, M. E., Avic, M. and Kavurmaci, H., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, arXiv:1202.0380v1[math.CA].
• [12] Park, J., Some new Hermite-Hadamard-like type inequalities on geometrically convex functions, Inter. J. of Math. Anal., 8(16) (2014),793-802.
• [13] Park, J., On Some Integral Inequalities for Twice Differentiable Quasi-Convex and Convex Functions via Fractional Integrals, Applied Mathematical Sciences, Vol. 9(62) (2015), 3057-3069 HIKARI Ltd, www.m-hikari.com. http://dx.doi.org/10.12988/ams.2015.53248.
• [14] Samko, S.G., Kilbas A.A. and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, 1993, ISBN 2881248640.
• [15] Sarikaya, M. Z. and Ogunmez, H., On new inequalities via Riemann-Liouville fractional integration, Abstract and applied analysis, 2012 (2012) 10 pages.
• [16] Sarikaya, M. Z., Set, E., Yaldiz, H. and Basak, N., Hermite- Hadamard's inequalities for fractional integrals and related frac- tional inequalities, Math. and Comput. Model., 2011 (2011).
• [17] Set, E., Sarikaya, M. Z. and  Ozdemir, M. E., Some Ostrowski's type Inequalities for functions whose second derivatives are s-convex in the second sense, arXiv:1006.24 88v1 [math. CA] 12 June 2010.
• [18] Set, E.,  Ozdemir, M. E., Sarikaya M. Z., Karako, F., Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals, Khayyam J. Math., 1(1) (2015) 62-70.
• [19] Toader, Gh., On a generalization of the convexity, Mathematica, 30(53) (1988), 83-87.
• [20] Tunc, M., On some new inequalities for convex functions, Turk. J. Math., 35(2011), 1-7.
• [21] Tunc, M. and Yildirim, H., On MT-Convexity, arXiv: 1205.5453 [math. CA] 24 May 2012

### Details

Subjects Engineering Articles October 15, 2016 October 16, 2017 July 6, 2016 Year 2016, Volume 4, Issue 2

### Cite

 Bibtex @research article { konuralpjournalmath344661, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2016}, volume = {4}, pages = {1 - 9}, doi = {}, title = {SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE \$\\varphi -\$CONVEX BY USING FRACTIONAL INTEGRALS}, key = {cite}, author = {Yıldırım, M. Esra and Akkurt, Abdullah and Yıldırım, Hüseyin} } APA Yıldırım, M. E. , Akkurt, A. & Yıldırım, H. (2016). SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS . Konuralp Journal of Mathematics (KJM) , 4 (2) , 1-9 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/27712/344661 MLA Yıldırım, M. E. , Akkurt, A. , Yıldırım, H. "SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS" . Konuralp Journal of Mathematics (KJM) 4 (2016 ): 1-9 Chicago Yıldırım, M. E. , Akkurt, A. , Yıldırım, H. "SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS". Konuralp Journal of Mathematics (KJM) 4 (2016 ): 1-9 RIS TY - JOUR T1 - SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS AU - M. Esra Yıldırım , Abdullah Akkurt , Hüseyin Yıldırım Y1 - 2016 PY - 2016 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 1 EP - 9 VL - 4 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2016 ER - EndNote %0 Konuralp Journal of Mathematics (KJM) SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS %A M. Esra Yıldırım , Abdullah Akkurt , Hüseyin Yıldırım %T SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS %D 2016 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 4 %N 2 %R %U ISNAD Yıldırım, M. Esra , Akkurt, Abdullah , Yıldırım, Hüseyin . "SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS". Konuralp Journal of Mathematics (KJM) 4 / 2 (October 2016): 1-9 . AMA Yıldırım M. E. , Akkurt A. , Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math.. 2016; 4(2): 1-9. Vancouver Yıldırım M. E. , Akkurt A. , Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics (KJM). 2016; 4(2): 1-9. IEEE M. E. Yıldırım , A. Akkurt and H. Yıldırım , "SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS", Konuralp Journal of Mathematics (KJM), vol. 4, no. 2, pp. 1-9, Oct. 2016
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