Abstract
Let S be a self-mapping on a normed space X. In this paper, we introduce three new classes of mappings satisfying the following conditions:
max(o <= k <= m) (k even)parallel to S-k x - S-k y parallel to = max(o <= k <= m k odd)parallel to S-k x - S-k y parallel to,
max(o <= k <= m.k even)parallel to S-k x - S-k y parallel to <= max(o <= k <= m k odd)parallel to S-k x - S-k y parallel to,
max(o <= k <= m.k even)parallel to S-k x - S-k y parallel to >= max(o <= k <= m k odd)parallel to S-k x - S-k y parallel to,
for all x, y is an element of X, where m is a positive integer. We prove some properties of these classes of mappings.