On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals

Mehmet Kunt; İmdat İşcan

doi:10.36753/mathenot.421462

EN

On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals

Abstract

In this paper, new Hermite-Hadamard-Fejer type integral inequalities for quasi-geometrically convex functions in fractional integral forms are obtained.

Keywords

Hermite-Hadamard inequality,Hermite-Hadamard-Fejer inequality,Hadamard fractional integral,quasigeometrically convex function

References

es [1] L. Fejér, Uber die Fourierreihen, II. Math. Naturwise. Anz Ungar. Akad., Wiss 24 (1906), 369-390, (in Hungarian).
[2] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann. J. Math. Pures Appl. 58 (1893), 171-215.
[3] İ. İşcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv preprint arXiv:1404.7722 (2014).
[4] İ. İşcan, Generalization of different type integral inequalities for s-convex functions via fractional integrals. Applicable Analysis(2013), doi: 10.1080/00036811.2013.851785.
[5] İ. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals. J. Inequal. Appl. (2013), 2013(491).
[6] İ. İşcan, On generalization of different type integral inequalities for s-convex functions via fractional integrals. Mathematical Sciences and Applications E-Notes 2(1) (2014), 55-67.
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[8] M. Kunt, İ. İşcan, On new inequalities of Hermite-Hadamard-Fejer type for GA-convex functions via fractional integrals. RGMIA Research Report Collection 18(2015), Article 108, 12 pp.
[9] M. A. Latif, S. S. Dragomir and E. Momaniat, Some Fejer type integral inequalities for geometricallyarithmetically-convex functions with applications. RGMIA Research Report Collection 18(2015), Article 25,18pp.
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[12] M.Z. Sarıkaya, On new Hermite Hadamard Fejér type integral inequalities. Stud. Univ. Babe¸s-Bolyai Math. 57(3) (2012), 377–386.
[13] Erhan Set, İ. İşcan, M. Zeki Sarikaya, M. Emin Ozdemir, On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals. Applied Mathematics and Computation 259 (2015) 875–881.
[14] K.-L. Tseng, G.-S. Yang and K.-C. Hsu, Some inequalities for differentiable mappings and applications to Fejér inequality and weighted trapezoidal formula. Taiwanese journal of Mathematics 15(4) (2011), 1737-1747.
[15] J. Wang, X. Li, M. Feckan and Y. Zhou, Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity. Appl. Anal. 92(11) (2012), 2241-2253. doi:10.1080/00036811.2012.727986.
[16] J. Wang, C. Zhu and Y. Zhou, New generalized Hermite-Hadamard type inequalities and applications to special means. J. Inequal. Appl. (2013), 2013(325), 15 pages.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mehmet Kunt

İmdat İşcan

Publication Date

October 30, 2016

Submission Date

July 22, 2015

Acceptance Date

-

Published in Issue

Year 2016 Volume: 4 Number: 2

DOI

https://doi.org/10.36753/mathenot.421462

IZ

https://izlik.org/JA42YF67BL

APA

Kunt, M., & İşcan, İ. (2016). On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Mathematical Sciences and Applications E-Notes, 4(2), 102-109. https://doi.org/10.36753/mathenot.421462

AMA

1.Kunt M, İşcan İ. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4(2):102-109. doi:10.36753/mathenot.421462

Chicago

Kunt, Mehmet, and İmdat İşcan. 2016. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4 (2): 102-9. https://doi.org/10.36753/mathenot.421462.

EndNote

Kunt M, İşcan İ (October 1, 2016) On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Mathematical Sciences and Applications E-Notes 4 2 102–109.

IEEE

[1]M. Kunt and İ. İşcan, “On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 102–109, Oct. 2016, doi: 10.36753/mathenot.421462.

ISNAD

Kunt, Mehmet - İşcan, İmdat. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes 4/2 (October 1, 2016): 102-109. https://doi.org/10.36753/mathenot.421462.

JAMA

1.Kunt M, İşcan İ. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016;4:102–109.

MLA

Kunt, Mehmet, and İmdat İşcan. “On New Inequalities of Hermite-Hadamard-Fejer Type for Quasi-Geometrically Convex Functions via Fractional Integrals”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, Oct. 2016, pp. 102-9, doi:10.36753/mathenot.421462.

Vancouver

1.Mehmet Kunt, İmdat İşcan. On new inequalities of Hermite-Hadamard-Fejer type for quasi-geometrically convex functions via fractional integrals. Math. Sci. Appl. E-Notes. 2016 Oct. 1;4(2):102-9. doi:10.36753/mathenot.421462

Cited By

A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Axioms

https://doi.org/10.3390/axioms12070719

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