Polynomial stability of evolution operators in Banach spaces
The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
On (h, k)-stability of evolution operators in Banach spaces
Abstract The main aim of this work is to define and exemplify various stability concepts and to emphasize connections between them. These stability concepts are included in a general concept, the so-called ( h , k ) -stability. We motivate our approach with illustrative examples.
Meromorphic function sharing a small function with a homogeneous differential polynomial
Abstract In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.