On exponential h-expansiveness of semigroups of operators in Banach spaces Original Research Article

This paper introduces the concept of exponential h-expansiveness for semigroups of nonlinear operators, which is an extension of classical concept of exponential expansiveness. Following the idea of obtaining an unitary treatment for stability and expansiveness, necessary and sufficient conditions for exponential h-expansiveness are given. As particular cases, the variants for exponential expansiveness of some well-known stability results due to Datko, Pazy, Ichikawa, Rolewicz and Neerven are obtained.