Some generalized Ostrowski type fractional integral inequalities for MT−convex functions with applications on special means
DOI:
https://doi.org/10.22199/issn.0717-6279-4102Keywords:
Ostrowski inequality, fractional integral, Katugampola fractional integral, MT−convex functionAbstract
Some generalized Ostrowski-type integral inequalities for r−times differentiable functions whose absolute values are MT−convex have been discussed. Moreover, some applications on special bivariate means are obtained.
References
S. S. Dragomir and S. Wang, “A new inequality of Ostrowski's type in L1 norm and applications to some special means and to some numerical quadrature rules”, Tamkang Journal of Mathematics, vol. 28, no. 3, pp. 239–244, 1997. https://doi.org/10.5556/j.tkjm.28.1997.4320
S. S. Dragomir and S. Wang, “Applications of ostrowski's inequality to the estimation of error bounds for some special means and for some numerical quadrature rules”, Applied Mathematics Letters, vol. 11, no. 1, pp. 105–109, 1998. https://doi.org/10.1016/s0893-9659(97)00142-0
G. Farid, U. N. Katugampola, and M. Usman, “Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals”, Studia Universitatis Babes-Bolyai Matematica, vol. 63, no. 4, pp. 465–474, 2018. https://doi.org/10.24193/subbmath.2018.4.04
G. Farid, U. N. Katugampola, and M. Usman, “Ostrowski type fractional integral inequalities for S-godunova-levin functions via Katugampola fractional integrals”, Open Journal of Mathematical Sciences, vol. 1, no. 1, pp. 97–110, 2017. https://doi.org/10.30538/oms2017.0010
S. Hussain, J. Khalid and F. Azhar, “Some generalized ostrowski type fractional integral inequalities for h−convex functions and related results”, (submitted).
J. Hadamard, “Essai sur l’etude des fonctions donnees par leur develoment de Taylor”, Journal de Mathématiques Pures et Appliquées, vol. 8, pp. 101-186, 1992.
U. N. Katugampola, “New approach to generalized fractional derivatives”, Bulletin of Mathematical Analysis and Applications, vol. 6, no. 4, 1-15, 2014.
U. N. Katugampola, “New approach to a generalized fractional integral”, Applied Mathematics and Computation, vol. 218, pp. 860-865, 2011. https://doi.org/10.1016/j.amc.2011.03.062
S. Kermausuor, Generalized “Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals”, Journal of Nonlinear Sciences and Applications, vol. 12, pp. 509-522, 2019. https://doi.org/10.22436/jnsa.012.08.02
S. M. Kaung, G. Farid, W. Nazeer and M. Usman, “Ostrowski type fractional integral inequalities for mappings whose derivatives are (α, m)−convex via Katugampola fractional integrals”, Nonlinear Functional Analysis and Applications, vol. 24, no. 1, pp. 109-126, 2019.
R. Khalil, A. Al Horani, A. Yousef and M. Sabadheh, “A new definition of Fractional derivative”, Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014. https://doi.org/10.1016/j.cam.2014.01.002
W. J. Liu, Q.-L. Xue and S. -F. Wang, “Several new perturbed Ostrowski-like type inequalities”, Journal of Inequalities in Pure and Applied Mathematics, vol. 8, no. 4, pp. 1-6, 2007.
W. J. Liu, W. S. Wen, J. K. Park, “Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals”, Journal of Nonlinear Sciences and Applications, vol. 9, pp. 766-777, 2016. https://doi.org/10.22436/jnsa.009.03.05
H. Laurent, “Sur le calcul des dérivées à indicies quelconques", Nouvelles annales de mathématiques, vol. 3, no. 3, pp. 240-252, 1884.
D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
S. Özcan and I. İ şcan, “Some new Hermite-Hadamard type inequalities for s−convex functions and their applications”, Journal of Inequalities and Applications, pp. 1-11, 2019. https://doi.org/10.1186/s13660-019-2151-2
S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and applications, Gordon and Breach Science Publishers, Yverdon, 1993.
M. Tunc, “Ostrowski type inequalities for functions whose derivatives are MT-convex”, Journal of Computational Analysis and Applications, vol. 17, no. 4, pp. 691-696, 2014.
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