On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function
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Authors
Mohamed Jleli
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Bessem Samet
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Abstract
In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with
respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals
and the Hadamard fractional integrals.
Share and Cite
ISRP Style
Mohamed Jleli, Bessem Samet, On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1252--1260
AMA Style
Jleli Mohamed, Samet Bessem, On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function. J. Nonlinear Sci. Appl. (2016); 9(3):1252--1260
Chicago/Turabian Style
Jleli, Mohamed, Samet, Bessem. "On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1252--1260
Keywords
- Hermite-Hadamard inequality
- fractional integral with respect to another function
- Riemann-Liouville fractional integral
- Hadamard fractional integral.
MSC
References
-
[1]
M. Alomari, M. Darus, U. S. Kirmaci , Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comput. Math. Appl., 59 (2010), 225-232.
-
[2]
A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Mat., 28 (1994), 7-12.
-
[3]
S. Belarbi, Z. Dahmani , On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math., 10 (2009), 5 pages.
-
[4]
J. de la Cal, J. Carcamob, L. Escauriaza, A general multidimensional Hermite-Hadamard type inequality, J. Math. Anal. Appl., 356 (2009), 659-663.
-
[5]
Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1 (2010), 51-58.
-
[6]
Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9 (2010), 493-497.
-
[7]
Z. Dahmani, L. Tabharit, S. Taf, New generalizations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2 (2010), 93-99.
-
[8]
S. S. Dragomir, On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan. J. Math., 5 (2001), 775-788.
-
[9]
S. S. Dragomir, Hermite-Hadamard's type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Linear Algebra Appl., 436 (2012), 1503-1515.
-
[10]
S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and totrapezoidal formula, Appl. Math. lett., 11 (1998), 91-95.
-
[11]
S. S. Dragomir, Y. J. Cho, S. S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. Math. Anal. Appl., 245 (2000), 489-501.
-
[12]
S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University (2000)
-
[13]
J. Hadamard, Étude sur les propriétés des fonctions entiéres et en particulier d'une fonction considérée par Riemann, J. Math. Pure Appl., 58 (1893), 171-216.
-
[14]
I. İşcan, New general integral inequalities for quasi-geometrically convex functions via fractional integrals, J. Inequal. Appl., 2013 (2013), 15 pages.
-
[15]
I. İşcan, On generalization of different type integral inequalities for s-convex functions via fractional integrals, Math. Sci. Appl., 2 (2014), 55-67.
-
[16]
A. A. Kilbas, O. I. Marichev, S. G. Samko, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Switzerland (1993)
-
[17]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
-
[18]
D. S. Mitrinović, I. B. Lacković, Hermite and convexity , Aequationes Math., 28 (1985), 229-232.
-
[19]
M. A. Noor, Hermite-Hadamard inequality for log-preinvex functions, J. Math. Anal. Approx. Theory, 2 (2007), 126-131.
-
[20]
M. A. Noor, K. I. Noor, M. U. Awan, Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput., 251 (2015), 675-679.
-
[21]
M. Z. Sarikaya, S. Erden, On the Hermite-Hadamard-Fejér type integral inequality for convex function, Turk. J. Anal. Number Theory, 2 (2014), 85-89.
-
[22]
M. Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstr. Appl. Anal., 2012 (2012), 10 pages.
-
[23]
M. Z. Sarikaya, E. Set, H. Yaldiz, N. Başak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modell., 57 (2013), 2403-2407.