In order to show novel generalizations of mathematical inequality, fractional integral operators are frequently used. Fractional used simulate a broad range scientific as well engineering phenomena such elasticity, viscous fluid, fracture mechanics, continuous population, equilibrium, visco-elastic deformation, heat conduction problems, and others. this manuscript, we introduce some notions gen...

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 ...

Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions.

In this paper, we introduce and study some new classes of invex sets preinvex functions with respect to an arbitrary function k the bifunction ?(.,.); which are called generalized functions. These nonconvex include function, convex k-convex as special cases. We properties It is shown that minimum on can be characterized by a class variational inequalities, directional variational-like inequalit...

*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...

New Hermite-Hadamard-type integral inequalities for φ-MT-preinvex functions are obtained. Our results in special cases yield some of those results proved in recent articles concerning with the differentiable MTconvex functions. Some applications to special means and the trapezoidal formula are also considered, respectively. c ©2016 All rights reserved.