Nonlinear (m, p)-Isometric And (2, p)-Concave Mappings on Complex Normed Spaces
Nonlinear (m, p)-Isometric And (2, p)-Concave Mappings on Complex Normed Spaces
Let $ S$ be a self mapping on a complex normed space ${\mathcal X}$. In this paper, we study the class of mappings satisfying the following condition$$ \sum_{0\leq k \leq m}(-1)^{m-k}\binom{m}{k}\big\|S^kx-S^ky\big\|^p=0,$$for all $x,y\in X$, where $m$ is a positive integer. We prove some of the properties of these classes of …