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

Abstract

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
There are 21 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

M. Esra Yıldırım This is me

Abdullah Akkurt

Hüseyin Yıldırım

Publication Date October 15, 2016
Submission Date October 16, 2017
Acceptance Date July 6, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

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, 4(2), 1-9.
AMA Yıldırım ME, Akkurt A, Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. October 2016;4(2):1-9.
Chicago Yıldırım, M. Esra, Abdullah Akkurt, and Hüseyin Yıldırım. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 1-9.
EndNote Yıldırım ME, Akkurt A, Yıldırım H (October 1, 2016) SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 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 J. Math., vol. 4, no. 2, pp. 1–9, 2016.
ISNAD Yıldırım, M. Esra et al. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (October 2016), 1-9.
JAMA Yıldırım ME, Akkurt A, Yıldırım H. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:1–9.
MLA Yıldırım, M. Esra et al. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 2, 2016, pp. 1-9.
Vancouver Yıldırım ME, 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.
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