Extensions of a fixed point theorem of Meir and Keeler - Project Euclid
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Extensions of a fixed point theorem of Meir and Keeler - Project Euclid
d(x, y) < ~+6 implies d(gx, gy) < ~. Meir and Keeler proved that an (e, 6)-contraction g of a complete metric space. X has a unique fixed point r/ in X and {g"x}2"= 1 ...
Extensions of a fixed point theorem of Meir and Keeler Sehie Park* and Jong Sook Bae
1. Introduction
Meir and Keeler [9] established a fixed point theorem which is a remarkable generalization of the Banach contraction principle. A selfmap g of a metric space (X, d) is called a weakly uniformly strict contraction or simply an (e, 6)-contraction if for each e > 0 , there exists a c5> 0 such that for all x, yEX, (1)
~ 0 , there exists 6 = 6 (~)>0 such that for all x, y~J(, (2)
e 0 and a subsequence {fx.,} o f {fx.} such that
d(fx.,,fx.,+l ) :~ 2e.
(5) By (2), there exists 0 N, we can find m such that ni 0 , there exists 6 > 0 such that for all x, yEX,
