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 determine the radius of λ -uniform convexity, id="M2"> -starlikeness, and id="M3"> α -convexity order id="M4"> δ for Weierstrass canonical product an entire function as a root having smallest modulus argument id="M5"> ϕ functional equation. As special cases, also id="M6"> id="...

In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now the non-convex algorithms lack convergence guarantee from the initial solution to the global optimum. This paper aims to provide theoretical guarantee for sparse recovery via non-convex optimization. The concept of weak convexity is incorporated into...

We study the evolution of convex complete non-compact graphs by positive powers Gauss curvature. show that if initial graph has a local uniform convexity, then evolves any power curvature for all time. In particular, is not necessarily differentiable.