Nonlinear (m, p)-Isometric And (2, p)-Concave Mappings on Complex Normed Spaces

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El Moctar Ould Beiba
Aydah Mohammed Ayed Al-Ahmadi

Abstract

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 mappings.

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