Schwarz type lemmas and their applications in Banach spaces

The main purpose of this paper is to develop some methods investigate the Schwarz type lemmas holomorphic mappings and pluriharmonic in Banach spaces. Initially, we extend classical spaces, then apply these extensions establish a sharp Bloch theorem for on homogeneous unit balls ℂn obtain boundary Furthermore, improve generalize planar harmonic into forms present applications Additionally, using relatively simple method proof, prove Schwarz–Pick estimates JB*-triples, obtained results provide improvements generalizations corresponding [9].