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Smallest and greatest fixed points of quasimonotone increasing mappings

โœ Scribed by Roland Uhl

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
140 KB
Volume
248-249
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abstract

In a Banach space E (pre)ordered by a cone we consider a mapping f : [v,w] โ†’ E (v,w โˆˆ E, v โ‰ค w) which satisfies v โ‰ค f(v) and f(w) โ‰ค w. We show that f has a smallest and a greatest fixed point, if it is continuous, quasimonotone increasing and condensing, in essence. Finally we admit discontinuities with upward jumps.

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## liitroduction In this paper we give common fixed point theorems for mappings fulfilling some nonlinear contraction type conditions on a 2-metric space. For the notions see 0 1. The concept of a %metric space (XI d ) has been investigated by S. GAHLER in [7]. For other papers on 2-metric spaces