(p,r)-Invex Sets and Functions

Generalized Invex Sets and Preinvex Functions on Riemannian Manifolds

In this paper, a geodesic α-invex subset of a Riemannian manifold is introduced. Geodesic α-invex and α-preinvex functions on a geodesic α-invex set with respect to particular maps are also defined. Further, we study the relationships between geodesic α-invex and α-preinvex functions on Riemannian manifolds. Some results of a non smooth geodesic α-preinvex function are also discussed using prox...

Invex sets and preinvex functions on Riemannian manifolds

The concept of a geodesic invex subset of a Riemannian manifold is introduced. Geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined. The relation between geodesic invexity and preinvexity of functions on manifolds is studied. Using proximal subdifferential, certain results concerning extremum points of a non smooth geodesic preinvex function ...

Generalized Differentiable -Invex Functions and Their Applications in Optimization

E-convex function was introduced by Youness 1 and revised by Yang 2 . Chen 3 introduced Semi-E-convex function and studied some of its properties. Syau and Lee 4 defined E-quasi-convex function, strictly E-quasi-convex function and studied some basic properties. Fulga and Preda 5 introduced the class of E-preinvex and E-prequasi-invex functions. All the above E-convex and generalized E-convex f...

On interval-valued optimization problems with generalized invex functions

*Correspondence: [email protected] 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia 2Permanent address: Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Full list of author information is available at the end of the article Abstract This paper is devoted to study interval-valued optimization p...

On Pre-θ-Open Sets and Two Classes of Functions