This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...

In this paper we present a bundle method for solving a generalized variational inequality problem. This problem consists in nding a zero of the sum of two multivalued operators de ned on a real Hilbert space. The rst one is monotone and the second one is the subdi erential of a lower semicontinuous proper convex function. The method is based on the auxiliary problem principle due to Cohen and t...

The training process for deep learning and pattern recognition normally involves the use of convex strongly optimization algorithms such as AdaBelief SAdam to handle lots “uninformative” samples that should be ignored, thus incurring extra calculations. To solve this open problem, we propose design bandit sampling method make these focus on “informative” during process. Our contribution is twof...

Strong restricted-orientation convexity is a generalization of standard convexity. We explore the properties of strongly convex sets in multidimensional Euclidean space and identify major properties of standard convex sets that also hold for strong convexity. We characterize strongly convex flats and halfspaces, and establish the strong convexity of the affine hull of a strongly convex set. We ...