The left Riemann-Liouville fractional Hermite-Hadamard type inequalities for convex functions
-
Mehmet Kunt
,
Dünya Karapinar
Abstract
In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.
(Communicated by Ján Borsík)
References
[1] Dragomir, S. S.—Agarwal, R. P.: Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11(5) (1998), 91–95.10.1016/S0893-9659(98)00086-XSuche in Google Scholar
[2] Hadamard, J.: Étude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl. 58 (1893), 171–215.Suche in Google Scholar
[3] Hermite, Ch.: Sur deux limites ďune intégrale définie, Mathesis 3 (1883), 82–83.Suche in Google Scholar
[4] Kirmaci, U. S.: Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (2004) 137–146.10.1016/S0096-3003(02)00657-4Suche in Google Scholar
[5] Kilbas, A. A.—Srivastava, H. M.—Trujillo, J. J.: Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.Suche in Google Scholar
[6] Pearce, C. E. M.—Pecaric, J.: Inequalities for differentiable mappings with application to special means and quadrature formulae, Appl. Math. Lett. 13 (2000), 51–55.10.1016/S0893-9659(99)00164-0Suche in Google Scholar
[7] Roberts, A. W.—Varberg, D. E.: Convex Functions, Academic Press, New York, 1973.Suche in Google Scholar
[8] Sarikaya, M. Z.—Set, E.—Yaldiz, H.—Başak, N.: Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Mod. 57(9) 2013), 2403–2407.10.1016/j.mcm.2011.12.048Suche in Google Scholar
[9] Zhou, Z.: Basic Theory of Fractional Differential Equations, World Scientific, New Jersey, 2014.10.1142/9069Suche in Google Scholar
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Artikel in diesem Heft
- Regular papers
- On the finite embeddability property for quantum B-algebras
- A dual Ramsey theorem for finite ordered oriented graphs
- On EMV-Semirings
- A nonsymmetrical matrix and its factorizations
- On weakly 𝓗-permutable subgroups of finite groups
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- A geometrical version of Hardy-Rellich type inequalities
- On a Choquet-Stieltjes type integral on intervals
- Uniqueness of meromorphic functions sharing four small functions on annuli
- A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator
- Functions of bounded variation related to domains bounded by conic sections
- Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables
- Oscillatory criteria for the second order linear ordinary differential equations
- When deviation happens between rough statistical convergence and rough weighted statistical convergence
- The retraction of certain banach right modules associated to a character
- On sequence spaces generated by binomial difference operator of fractional order
- Some refinements of young type inequality for positive linear map
- On the Gromov-Hausdorff limit of metric spaces
- The beta exponentiated Nadarajah-Haghighi distribution: theory, regression model and application
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