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Hermite-hadamard inequalities type for raina’s fractional integral operator using η−convex functions

  • HERNÁNDEZ H., JORGE E. [1] ; VIVAS-CORTEZ, MIGUEL [2]
    1. [1] Universidad Centroccidental Lisandro Alvarado

      Universidad Centroccidental Lisandro Alvarado

      Venezuela

    2. [2] Pontificia Universidad Católica del Ecuador

      Pontificia Universidad Católica del Ecuador

      Quito, Ecuador

  • Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 26, Nº. 1, 2019, págs. 1-20
  • Idioma: inglés
  • DOI: 10.15517/rmta.v26i1.36214
  • Enlaces
  • Resumen
    • In the present work, it is obtained some results concerning the integralinequality of Hermite-Hadamard, and others related to it, using η−convexfunctions and the fractional integral operator defined by R.K. Raina.

  • Referencias bibliográficas
    • [1] Agarwal, R.P.; Luo, M-J.; Raina, R.K. (2016) “On Ostrowski type inequalities”, Fasciculi Mathematici 56(1): 5–27.
    • [2] Bai, R.; Qi, F.; Xi, B. (2013) “Hermite-Hadamard type inequalities for them− and (α, m)−logarithmically convex functions”, Filomat 27(1):...
    • [3] Dragomir, S.S.; Pecaric, J.; Persson; L. (1995) “Some inequalities ofHadamard type”, Soochow Journal of Mathematics 21(3): 335–341.
    • [4] Dragomir, S.S.; Pearce, C.E.M. (2002) Selected Topics on HermiteHadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
    • [5] Gordji, M.E.; Delavar, M.R.; Dragomir, S.S. (2015) “Some inequality related to η-convex function”, Preprint, RGMIA ResearchReportCollection.
    • [6] Eshaghi, M.; Dragomir, S.S.; Delavar, M.R. (2015) “An inequality related to η−convex functions”, International Journal of Nonlinear Analysis...
    • [7] Hadamard, J. (1893) “Etude sur les propriétés des fonctions entières et en particulier d’une fonction considérée par Riemann”, Journal...
    • [8] Iqbal, M.; Iqbal, M.; Nazeer, K. (2015) “Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals”,...
    • [9] Khan, M.A.; Khurshid, Y.; Ali, T. (2017) “Hermite-Hadamard inequality for fractional integrals via η−convex functions”, Acta Mathematica...
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    • [11] Özdemir, M.E.; Akdemir, A.O.; Set, E. (2016) “On (h, m)−Convexity and Hadamard Type Inequalities”, Transylvanian Journal of Mathematics...
    • [12] Raina, R.K. (2005) “On Generalized Wright’s Hypergeometric Functions and Fractional Calculus Operators", East Asian Mathematics Journal...
    • [13] Sarikaya, M.Z.; Set, E.; Yaldiz, H.; Basak, N. (2013) “Hermite-Hadamard’s inequalities for fractional integrals and related fractional...
    • [14] Set, E.; Çelik, B.; Akdemir, A.O. (2017) “Some new Hermite-Hadamard type inequalities for quasi-convex functions via fractional integral...

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