in this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

*Correspondence: [email protected] 1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China Full list of author information is available at the end of the article Abstract With the equivalent relationships between the G-generalized invexities and general invexities on the hand, we present two characterizations for G-preinvexity; we also discuss the relationships...

In this paper‎, ‎making use of a new identity‎, ‎we establish new‎ ‎inequalities of Ostrowski type for the class of preinvex functions and‎ ‎gave some midpoint type inequalities‎.

Convexity and generalized convexity play a central role in mathematical economics, engineering, and optimization theory. Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming (see [1–4, 6–11] and the references therein). Weir and Mond [7] and Weir and Jeyakumar [6] introduced the definition of preinvexity for the scalar f...

In this paper, we extend the class of strongly $ E $-preinvex and $-invex functions to quasi $-preinvex, pseudo functions. Some non-trivial suitable examples have been constructed in support our definitions. Several interesting properties relationships these are discussed. Furthermore, show application results, consider a non-linear programming problem that local minimum point is also strictly ...