In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The interand intraspecies interactions may be either repulsive or attractive. The main effects considered here are spontaneous breaking of the symmetry between components in symmetric and antisymmetric solitons, and spatial splitting bet...