Fractional Ostrowski type inequalities for functions whose derivatives are s-preinvex
Palabras clave:
integral inequality, -preinvex functions, Hölder inequality, power mean inequalityResumen
In this paper, we establish a new integral identity, and then we derive some new fractional Ostrowski type inequalities for functions whose derivatives
are s-preinvex.
Descargas
Referencias
W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen (german), Publ. Inst. Math. (Beograd) (N.S.) 23(37) (1978), 13 – 20.
R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, in “ Fractals and Fractional Calculus in Continuum Mechanics ” (Papers from the CISM Course on Scaling Laws and Fractality in Continuum Mechanics held in Udine, September 23--27, 1996; edited by A. Carpinteri and F. Mainardi.), CISM Courses and Lect. 378, Springer-Verlag, Vienna, 1997, 223 – 276.
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, “ Theory and Applications of Fractional Differential Equations ”, North-Holland Mathematics Studies 204, Elsevier Science B.V., Amsterdam, 2006.
U.S. Kirmaci, M.E. Özdemir, Some inequalities for mappings whose derivatives are bounded and applications to special means of real numbers, Appl. Math. Lett. 17 (6) (2004), 641 – 645.
J.-Y. Li, On Hadamard-type inequalities for s-preinvex functions, J. Chongqing Norm. Univ. Nat. Sci. Ed. 27 (4) (2010), p. 003.
W. Liu, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Math. Notes 16 (1) (2015), 249 – 256.
W. Liu, Some Ostrowski type inequalities via Riemann-Liouville fractional integrals for h-convex functions, J. Comput. Anal. Appl. 16 (5) (2014), 998 – 1004.
B. Meftah, Hermite-Hadamard’s inequalities for functions whose first derivatives are (s, m)-preinvex in the second sense, JNT 10 (2016), 54 – 65.
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, Some new Ostrowski’s inequalities for functions whose nth derivatives are r-Convex, Int. J. Anal. 2016, Art. ID 6749213, 7 pp.
B. Meftah, New Ostrowski’s inequalities, Rev. Colombiana Mat. 51 (1) (2017), 57 – 69.
B. Meftah, Ostrowski inequality for functions whose first derivatives are s-preinvex in the second sense, Khayyam J. Math. 3 (1) (2017), 61 – 80.
B. Meftah, Fractional Ostrowski type inequalities for functions whose first derivatives are φ-preinvex, J. Adv. Math. Stud. 10 (3) (2017), 335 – 347.
B. Meftah, Some new Ostrowski’s inequalities for n-times differentiable mappings which are quasi-convex, Facta Univ. Ser. Math. Inform. 32 (3) (2017), 319 – 327.
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 (2) (2017), 146 – 154.
B. Meftah, Some new Ostrowski’s inequalities for functions whose nth derivatives are logarithmically convex, Ann. Math. Sil. 32 (1) (2018), 275 – 284.
K.S. Miller, B. Ross, “ An Introduction to the Fractional Calculus and Fractional Differential Equations ”,John Wiley & Sons, Inc., New York, 1993.
S.R. Mohan, S.K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl. 189 (3) (1995), 901 – 908.
M.A. Noor, K.I. Noor, M.U. Awan, Fractional Ostrowski inequalities for s-Godunova-Levin functions, International Journal of Analysis and Applications , 5 (2) (2014), 167 – 173.
M.A. Noor, K.I. Noor, M.U. Awan, Fractional Ostrowski inequalities for (s, m)-Godunova-Levin functions, Facta Univ. Ser. Math. Inform. 30 (4) (2015), 489–499.
A. Ostrowski, Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert (german), Comment. Math. Helv. 10 (1) (1937), 226 – 227.
J. Park, Hermite-Hadamard-like type inequalities for s-convex function and s-Godunova-Levin functions of two kinds, Int. Math. Forum 9 (2015), 3431 – 3447.
J.E. Pečarić, F. Proschan, Y.L. Tong, “ Convex Functions, Partial Orderings, and Statistical Applications ”, Mathematics in Science and Engineering 187, Academic Press, Inc., Boston, MA, 1992.
M.Z. Sarikaya, H. Filiz, Note on the Ostrowski type inequalities for fractional integrals, Vietnam J. Math. 42 (2) (2014), 187 – 190.
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 (7) (2012), 1147 – 1154.
T. Weir, B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1) (1988), 29 – 38.
C. Zhu, M. Fečkan, J. Wang, Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula, J. Appl. Math. Stat. Inf. 8 (2) (2012), 21 – 28.
