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BEST PROXIMITY POINTS AND FIXED POINTS WITH $R$-FUNCTIONS IN THE FRAMEWORK OF $w$-DISTANCES
Part of
- Nonlinear operators and their properties
- Connections with other structures, applications
ALEKSANDAR KOSTIĆ, ERDAL KARAPINAR, VLADIMIR RAKOČEVIĆ
Journal:

Bulletin of the Australian Mathematical Society / Volume 99 / Issue 3 / June 2019

Published online by Cambridge University Press:

17 December 2018, pp. 497-507

Print publication:

June 2019
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We study best proximity points in the framework of metric spaces with $w$-distances. The results extend, generalise and unify several well-known fixed point results in the literature.

FIXED POINTS THEOREMS FOR GENERALISED WEAKLY CONTRACTIVE MAPPINGS
Part of
- Nonlinear operators and their properties
- Connections with other structures, applications
ZHIQUN XUE
Journal:

Bulletin of the Australian Mathematical Society / Volume 93 / Issue 2 / April 2016

Published online by Cambridge University Press:

04 September 2015, pp. 321-329

Print publication:

April 2016
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In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results.

Coincidence Sets of Coincidence Producing Maps
Helga Schirmer
Journal:

Canadian Mathematical Bulletin / Volume 26 / Issue 2 / 01 June 1983

Published online by Cambridge University Press:

20 November 2018, pp. 167-170

Print publication:

01 June 1983
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A theorem by H. Robbins shows that every closed and non-empty subset of the unit ball Bn in Euclidean n-space is the fixed point set of a self map of Bn. This result is extended to coincidence producing maps of Bn, where a map ƒ:X → Y is coincidence producing (or universal) if it has a coincidence with every map g:X → Y. The main result implies that if ƒ:Bn, Sn - 1 → Bn, Sn - 1 is coincidence producing and A⊂Bn closed and nonempty, then there exist a map ƒ': Bn, Sn - 1 → Bn, Sn - 1 and a map g: Bn → Bn such that ƒ' | Sn - 1 is homotopic to ƒ | Sn-1 and A is the coincidence set of ƒ' and g.

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