Ostrowski Type Fractional Integral Inequalities for Generalized (g, s, m, φ)-Preinvex Functions
Keywords:
Ostrowski type inequality, Hölder’s inequality, power mean inequality, Riemann-Liouville fractional integral, s-convex function in the second sense, m-invex, P -functionAbstract
In the present paper, a new class of generalized (g, s, m, φ)-preinvex function is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (g, s, m, φ)-preinvex functions are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (g, s, m, φ)-preinvex functions via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given.
Downloads
References
T. S. Du, J. G. Liao, Y. J. Li, Properties and integral inequalities of Hadamard-Simpson type for the generalized (s, m)-preinvex functions, J. Nonlinear Sci. Appl. 9 (5) (2016), 3112 – 3126.
S. S. Dragomir, J. Pečarić, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (3) (1995), 335 – 341.
H. Hudzik, L. Maligranda, Some remarks on s-convex functions, Aequationes Math. 48 (1) (1994), 100 – 111.
T. Antczak, Mean value in invexity analysis, Nonlinear Anal. 60 (8) (2005), 1473 – 1484.
X. M. Yang, X. Q. Yang, K. L. Teo, Generalized invexity and generalized invariant monotonicity, J. Optim. Theory Appl. 117 (3) (2003), 607 – 625.
R. Pini, Invexity and generalized convexity, Optimization. 22 (4) (1991), 513 – 525.
D. D. Stancu, G. Coman, P. Blaga, “Analiză Numerică şi Teoria Aproximării”, Vol. II, Presa Universitară Clujeană, Cluj-Napoca, 2002.
W. Liu, New integral inequalities involving beta function via P -convexity, Miskolc Math Notes. 15 (2) (2014), 585 – 591.
M. E. Özdemir, E. Set, M. Alomari, Integral inequalities via several kinds of convexity, Creat. Math. Inform. 20 (1) (2011), 62 – 73.
W. Liu, W. Wen, J. Park, Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals, J. Nonlinear Sci. Appl. 9 (3) (2016), 766 – 777.
W. Liu, Ostrowski type fractional integral inequalities for MT-convex functions, Miskolc Mathematical Notes. 16 (1) (2015), 249 – 256.
M. Tunç, Ostrowski type inequalities for functions whose derivatives are MT-convex, J. Comput. Anal. Appl. 17 (4) (2014), 691 – 696.
P. S. Bullen, “Handbook of Means and Their Inequalities”, Kluwer Academic Publishers Group, Dordrecht, 2003.
