New Integral Inequalities through Invexity with Applications
Main Article Content
Abstract
In this paper, we obtain some inequalities of Simpson's inequality type for functions whose derivatives absolute values are quasi-preinvex function. Applications to some special means are considered.
Article Details
References
- S. S. Dragomir, R. P. Agarwal, and P. Cerone, On Simpson's inequality and applications, Journal of Inequalities and Applications, 5 (2000), 33-579.
- U.S. Kirmaci, Inequalities for differentiable mappings and applicatios to special means of real numbers to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
- T. Weir, and B. Mond, Preinvex functions in multiple bjective optimization, Journal of Mathematical Analysis and Applications, 136 (1998) 29-38.
- S. R. Mohan and S. K. Neogy, On invex sets and preinvex function, J. Math. Anal. Appl. 189 (1995), 901-908.
- A. Barani, S. Barani and S.S. Dragomir, Simpson's Type Inequalities for Functions Whose Third Derivatives in the Absolute Values are P-Convex , RGMIA Res. Rep. Coll., 14 (2011).
- M.Z. Sarikaya, E. Set and M.E. ¨Ozdemir, On new inequalities of Simpson's type for s-convex functions, Comput. Math. Appl. 60 (2010) 2191-2199.
- M. Alomari and M. Darus, “On some inequalities of Simpson-type via quasi-convex functions and applications,” Transylvanian Journal of Mathematics and Mechanics, 2 (2010), 15-24.
- X.M. Yang, X.Q. Yang and K.L. Teo, Characterizations and applications of prequasiinvex functions, properties of preinvex functions, J. Optim. Theo. Appl. 110 (2001) 645-668.
- P.S. Bullen, Handbook of Means and Their Inequalities, Kluwer Academic Publishers, Dordrecht, 2003.