N-Quasi-m-contractive and n-quasi-m-expansive operators on a Hilbert space

Abstract

In this paper, we introduce a new class of operators called the [Formula: see text]-quasi-[Formula: see text]-contractive and [Formula: see text]-quasi-[Formula: see text]-expansive operators which are generalizations of [Formula: see text]-quasi-[Formula: see text]-isometric operators on Hilbert space introduced by Mecheri and Prasad, in [S. Mecheri and T. Prasad, On n-quasi-m-isometric operators, Asian-Eur. J. Math. 9(4) (2016) 1650073]. In addition, we apply those classes to the weighted composition operator. We discuss some examples concerning those classes and the weighted composition operator.