关于k-折对称点的近于凸函数和拟凸函数子类的邻域

On the neighborhoods of certain subclasses of close-to-convex and quasi-convex

摘要: 研究了关于k-折对称点的近于凸函数和拟凸函数子类的邻域。对于 \mathcal S_s,\ n^(k)A, B 或者 \mathcal C_s,\ n^(k)A, B中的函数f, 得到了使得所有函数g\in\mathcal N_\delta(f)包含在 \mathcal S_s,\ n^(k)A, B内的充分条件，且 \delta 是最好的可能。

Abstract: The neighborhoods of certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points are studied. If f is in \mathcal S_s,\ n^(k)A, B or \mathcal C_s,\ n^(k)A, B, some sufficient conditions are established such that all functions g\in\mathcal N_\delta(f) are included in \mathcal S_s,\ n^(k)A, B with this \delta being the best possibility. Some of the results, presented in this paper, generalize and extend the corresponding results existing in some literatures.