|
|||||
|
|
|
|
|
|
|
|
|
Characterizations of
certain maps of contractive type
Chi Song Wong |
|
Vol. 68 (1977), No. 1, 293–296
|
Abstract |
|
The following result is obtained. Let f be a self map on a nonempty complete metric space (X,d). Then the following conditions are equivalent: (i) For any 𝜖 > 0, there exists δ(𝜖) > 0 such that d(f(x),f(y)) < 𝜖 whenever 𝜖 ≦ d(x,y) < 𝜖 + δ(𝜖). (ii) There exists a function w of [0,∞) into [0,∞) such that w(s) > s for all s > 0, w is lower semicontinuous from the right on (0,∞) and w(d(f(x),f(y))) ≦ d(x,y),x,y ∈ X. |
Mathematical Subject Classification 2000
Primary: 54E40
|
Milestones
Received: 21 October 1975
Revised: 16 July 1976
Published: 1 January 1977
|
Authors |
| Chi Song Wong | |
|
