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### Fractional Ostrowski Type Inequalities for Functions Whose Mixed Derivatives are Prequasiinvex and alpha-Prequasiinvex Functions

#### Abstract

In this paper, the authors introduce two new classes of generalized convex

functions of two independent variables, and establish a new integral

identity, from which they derive some new fractional Ostrowski's integral

inequalities for functions whose second derivatives are in these new classes

of functions.

#### Full Text:

PDF#### References

W. Alshanti, and A. Qayyum, A Note On New Ostrowski Type

Inequalities Using A Generalized Kernel, Bulletin of Mathematical Analysis

and Applications. 9 (2017), no.1, 1-18.

N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality

for double integrals and applications for cubature formulae. Soochow J.

Math. 27 (2001), no. 1, 1--10.

G. Farid, Some new Ostrowski type inequalities via fractional

integrals. Int. J. Anal. App., 14 (2017), no. 1, 64-68.

A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and

applications of fractional differential equations. North-Holland Mathematics

Studies, 204. Elsevier Science B.V., Amsterdam, 2006.

M. A. Latif, S. Hussain and S. S. Dragomir, Refinements of

Hermite-Hadamard-type inequalities for co-ordinated quasi-convex functions.

International Journal of Mathematical Archive. 3 (2012), no 1, 161-171.

M. A. Latif and S. Hussain, New inequalities of Ostrowski type

for co-ordineted convex functions via fractional integrals. J. Fract. Calc.

Appl. 2 (2012), no. 9, 1-15.

M. Matloka, On some Hadamard-type inequalities for $(h_{1},h_{2})$%

-preinvex functions on the co-ordinates. J. Inequal. Appl. 2013, 2013:227,

pp.

B. Meftah, Some New Ostrwoski's Inequalities for Functions Whose

nth Derivatives are $r$-Convex. International Journal of Analysis, 2016, 7

pages.

B. Meftah, Ostrowski inequalities for functions whose first

derivatives are logarithmically preinvex. Chin. J. Math. (N.Y.) 2016, Art.

ID 5292603, 10 pp.

B. Meftah, New Ostrowski's inequalities. Rev. Colombiana Mat. 51

(2017), no. 1, 57--69.

B. Meftah, Ostrowski inequality for functions whose first

derivatives are $s$-preinvex in the second sense. Khayyam J. Math. 3 (2017),

no. 1, 61--80.

B. Meftah, Fractional Ostrowski type inequalities for functions

whose first derivatives are $s$-preinvex in the second sense. International

Journal of Analysis and Applications 15 (2017), no. 2, 146--154.

bibitem{} B. Meftah, Some new Ostrowski's inequalities for n-times

differentiable mappings which are quasi-convex. Facta Univ. Ser. Math.

Inform. 32 (2017), no. 3, 319--327.

B. Meftah, Fractional Ostrowski type inequalities for functions

whose first derivatives are $varphi $-preinvex. J. Adv. Math. Stud. 10

(2017), no. 3, 335-347.

B. Meftah , Some new Ostrowski inequalities for functions whose $%

n^{th}$ derivatives are logarithmically convex. Ann. Math. Sil. De Gruyter

Open.

A. Ostrowski, Alexander, "{U}ber die Absolutabweichung einer

differentiierbaren Funktion von ihrem Integralmittelwert. (German) Comment.

Math. Helv. 10 (1937), no. 1, 226--227.

M. E. "{O}zdemir, H. Kavurmaci and E. Set, Ostrowski's type

inequalities for $(alpha ,m)$-convex functions. Kyungpook Math. J. 50

(2010), no. 3, 371--378.

B. G. Pachpatte, A new Ostrowski type inequality for double

integrals. Soochow J. Math. 32 (2006), no. 2, 317--322.

M. Z. Sarikaya, On the Ostrowski type integral inequality. Acta

Math. Univ. Comenian. (N.S.) 79 (2010), no. 1, 129--134.

M. Z. Sarikaya and H. Ogunmez, On the weighted Ostrowski-type

integral inequality for double integrals. Arab. J. Sci. Eng. 36 (2011), no.

, 1153--1160.

M. Z. Sari kaya, On the Hermite-Hadamard-type inequalities for

co-ordinated convex function via fractional integrals. Integral Transforms

Spec. Funct. 25 (2014), no. 2, 134--147.

E. Set, New inequalities of Ostrowski type for mappings whose

derivatives are $s$-convex in the second sense via fractional integrals.

Comput. Math. Appl. 63 (2012), no. 7, 1147--1154.

B. -Y. Xi, J. Sun, and S. -P. Bai, On some Hermite-Hadamard-type

integral inequalities for co-ordinated $left( alpha ,QCright) $- and $%

left( alpha ,CJright) $-convex functions. Tbilisi Math. J. 8 (2015), no.

, 75--86.

Q. Xue, J. Zhu and W. Liu, A new generalization of Ostrowski-type

inequality involving functions of two independent variables. Comput. Math.

Appl. 60 (2010), no. 8, 2219--2224.

DOI: https://doi.org/10.22342/jims.1.1.751.%25p

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