In this paper, we discusses the strong convexity, very convexity, near strong convexity, extremal convexity and (w) property, and the results generalize the corresponding results in refrence and so on.

In this paper, we discuss midpoint local uniform rotundity, weak local uniform rotundity and strong rotundity of Cesaro vector_valued sequence spaces cesp(Ek),and give their cirtieria.

If X * has (**) property,the Banach space X is strongly convex if and only if X is locally uniformly convex.

We give two necessary and sufficient conditions for n-Banach spaces to be uniformly convex spaces or strongly convex spaces.

A recession function of a positively homogenous function can be presented as an upper convex approximation,which can be used to study the optimality conditions of a class of nonsmooth optimization—directionally differentiable optimization.

On nearly extreme point and nearly strict convexity of quotient space;

The criterion of nearly extreme point in Orlicz function spaces are given, by the way we get the criterion of nearly strict convexity in the same spaces.

In this paper,integral transforms of functions belong to t he class are investigated,some results of a close to convex integral operator are given as well.