Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvex functions

Artion Kashuri, Rozana Liko


In the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvexfunctions via classical integrals and Riemann-Liouville fractional integrals are established. These results not only extends the results appeared in the literature (see [10], [11], [12]), but also provide new estimates on these types.

Palabras clave

Euler Gamma function; Euler Beta function; MT-convex function; Hermite-Hadamard type inequality; Ostrowski type inequality; Hölder’s inequality; power mean inequality; fractional integral; m-invex; P-function

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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, pp. 3112-3126, (2016).

S. S. Dragomir, J. Pečarić, L. E. Persson Some inequalities of Hadamard type Soochow J. Math., 21, pp. 335-341, (1995).

T. Antczak Mean value in invexity analysis Nonlinear Anal., 60, pp. 1473-1484, (2005).

X. M. Yang, X. Q. Yang, K. L. Teo Generalized invexity and generalized invariant monotonicity J. Optim. Theory Appl., 117, pp. 607-625, (2003).

R. Pini Invexity and generalized convexity Optimization., 22, pp. 513-525, (1991).

D. D. Stancu, G. Coman, P. Blaga Analiză numerică şi teoria aproximării Cluj-Napoca: Presa Universitară Clujeană, Vol. II, (2002).

W. Liu New integral inequalities involving beta function via P - convexity Miskolc Math Notes., 15, 2, pp. 585-591, (2014).

M. E. Özdemir, E. Set, M. Alomari Integral inequalities via several kinds of convexity Creat. Math. Inform., 20, 1, pp. 62-73, (2011).

H. Kavurmaci, M. Avci, M. E. Özdemir New inequalities of Hermite-Hadamard type for convex functions with applications arXiv:1006.1593v1 [math. CA], pp. 1-10, (2010).

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, pp. 766-777, (2016).

W. Liu, W. Wen, J. Park Ostrowski type fractional integral inequalities for MT-convex functions Miskolc Mathematical Notes., 16, 1, pp. 249-256, (2015).

M. Tunç Ostrowski type inequalities for functions whose derivatives are MT-convex J. Comput. Anal. Appl., 17, 4, pp. 691-696, (2014).


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