Research Article

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

Volume: 4 Number: 2 October 15, 2016
EN

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

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.

Keywords

References

  1. [1] Beckenbach, E. F., Convex functions, Bull. Amer. Math. Soc., 54(1948), 439-460.
  2. [2] Dahmani, Z. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(2010), no. 1, 51-58.
  3. [3] Dragomir, S. S., Inequalities of Jensen type for '-convex functions, Fasc. Math. 55(2015), 35-52.
  4. [4] Hudzik H. and Maligranda, L. Some remarks on s-convex functions, Aequationes Math., 48(1994), no. 1, 100-111.
  5. [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. [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. [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. [8] Işcan, I., On generalization of different type integral inequalities for s-convex functions via fractional integrals presented

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

M. Esra Yıldırım This is me
Türkiye

Publication Date

October 15, 2016

Submission Date

October 16, 2017

Acceptance Date

July 6, 2016

Published in Issue

Year 2016 Volume: 4 Number: 2

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. https://izlik.org/JA88MG74PK
AMA
1.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. https://izlik.org/JA88MG74PK
Chicago
Yıldırım, M. Esra, Abdullah Akkurt, and Hüseyin Yıldırım. 2016. “SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4 (2): 1-9. https://izlik.org/JA88MG74PK.
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
[1]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, Oct. 2016, [Online]. Available: https://izlik.org/JA88MG74PK
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 4/2 (October 1, 2016): 1-9. https://izlik.org/JA88MG74PK.
JAMA
1.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, Oct. 2016, pp. 1-9, https://izlik.org/JA88MG74PK.
Vancouver
1.M. Esra Yıldırım, Abdullah Akkurt, Hüseyin Yıldırım. SOME INTEGRAL INEQUALITIES FOR FUNCTIONS WHOSE SECOND DERIVATIVES ARE $\varphi -$CONVEX BY USING FRACTIONAL INTEGRALS. Konuralp J. Math. [Internet]. 2016 Oct. 1;4(2):1-9. Available from: https://izlik.org/JA88MG74PK
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