Abstract
The purpose of the present paper is to give some results related to classes of mappings, known as (m, p) - (hyper) expansive and (m, p) - (hyper) contractive acting on a metric space X.Amapping T : X -> X is (m, p) - expansive (respectively,(m, p) - contractive) for some metric d, integer m >= 1 and p is an element of (0, infinity) if, for any x, y is an element of X;
Sigma(0 <= k <= m) (-1)(k)((m)(k)) d (T(k)x, T(k)y)(p) <= 0(respectively >= 0)
and it is (m, p) -hyperexpansive (respectively, (m, p) - hypercontractive) if, for all x,y is an element of X
Sigma(0 <= k <= m) (-1)(k)((l)(k)) d (T(k)x, T(k)y)(p) <= 0(respectively >= 0), for l is an element of{1, 2, ...,m)
The notions of ( m, p)-expansive mapping or of ( m, p)-contractive mapping on a metric space generalize the notion of m - isometry for bounded linear operators