ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS

İMDAT İşcan

doi:10.36753/mathenot.207633

EN

ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS

Abstract

In this paper, a new general identity for differentiable mappingsvia Riemann-Liouville fractional integrals has been defined. By using of thisidentity, author has obtained new estimates on generalization of Hadamard,Ostrowski and Simpson type inequalities for functions whose derivatives inabsolutely value at certain powers are s-convex in the second sense

Keywords

Hermite-Hadamard inequality, Riemann-Liouville fractional integral,Ostrowski inequality, Simpson type inequality, s-convex function

References

M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, 1965.
M. Alomari, M. Darus and S.S. Dragomir, P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense. Appl. Math. Lett. 23 (2010), 1071–1076. [3] M. Alomari, M. Darus and U.S. Kirmaci, Some inequalities of Hermite-Hadamard type for s-convex functions. Acta Math. Sci. 31B(4) (2011), 1643–1652.
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J. Peˇcari´c, F. Proschan and Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications. Academic Press Inc.,1992.
M.Z. Sarıkaya and N. Aktan, On the generalization of some integral inequalities and their applications. Math. Comput. Modelling. 54 (2011), 2175- 2182.
M.Z. Sarıkaya, E. Set and M.E. Ozdemir, On new inequalities of Simpson’s type for s-convex functions. Computers and Math. with Appl. 60 (2010), 2191-2199.
M.Z. Sarıkaya, E. Set, H. Yaldız and N. Ba¸sak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Modelling. 57(9) (2013), 2403- 2407. doi:10.1016/j.mcm.2011.12.048.
Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Gire- sun, Turkey
E-mail address: imdat.iscan@giresun.edu.tr

Details

Primary Language

English

Subjects

-

Journal Section

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Authors

İMDAT İşcan This is me

Publication Date

June 1, 2014

Submission Date

March 9, 2015

Acceptance Date

-

Published in Issue

Year 2014 Volume: 2 Number: 1

DOI

https://doi.org/10.36753/mathenot.207633

IZ

https://izlik.org/JA92YR28CF

APA

İşcan, İ. (2014). ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS. Mathematical Sciences and Applications E-Notes, 2(1), 55-67. https://doi.org/10.36753/mathenot.207633

AMA

1.İşcan İ. ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS. Math. Sci. Appl. E-Notes. 2014;2(1):55-67. doi:10.36753/mathenot.207633

Chicago

İşcan, İMDAT. 2014. “ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR S-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS”. Mathematical Sciences and Applications E-Notes 2 (1): 55-67. https://doi.org/10.36753/mathenot.207633.

EndNote

İşcan İ (June 1, 2014) ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS. Mathematical Sciences and Applications E-Notes 2 1 55–67.

IEEE

[1]İ. İşcan, “ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS”, Math. Sci. Appl. E-Notes, vol. 2, no. 1, pp. 55–67, June 2014, doi: 10.36753/mathenot.207633.

ISNAD

İşcan, İMDAT. “ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR S-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS”. Mathematical Sciences and Applications E-Notes 2/1 (June 1, 2014): 55-67. https://doi.org/10.36753/mathenot.207633.

JAMA

1.İşcan İ. ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS. Math. Sci. Appl. E-Notes. 2014;2:55–67.

MLA

İşcan, İMDAT. “ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR S-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS”. Mathematical Sciences and Applications E-Notes, vol. 2, no. 1, June 2014, pp. 55-67, doi:10.36753/mathenot.207633.

Vancouver

1.İMDAT İşcan. ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS. Math. Sci. Appl. E-Notes. 2014 Jun. 1;2(1):55-67. doi:10.36753/mathenot.207633

Some New Hermite-Hadamard-Fejér Fractional Type Inequalities for h-Convex and Harmonically h-Convex Interval-Valued Functions

Mathematics

https://doi.org/10.3390/math10010074

New Hermite–Hadamard Integral Inequalities for Geometrically Convex Functions via Generalized Weighted Fractional Operator

Symmetry

https://doi.org/10.3390/sym14071440

INDEXING & ABSTRACTING & ARCHIVING

20477 The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS

ON GENERALIZATION OF DIFFERENT TYPE INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS VIAFRACTIONAL INTEGRALS

Abstract

Keywords

Abstract

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