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Abbas, Mujahid; Ali, Basit; Romaguera, Salvador

Generalized contraction and invariant approximation results on nonconvex subsets of normed spaces. (English) Zbl 1472.47041

Abstr. Appl. Anal. 2014, Article ID 391952, 5 p. (2014).
Summary: D. Wardowski [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)] introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized \(F\)-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

Cited in 3 Documents

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
41A50 Best approximation, Chebyshev systems

Keywords:

generalized \(F\)-contraction mappings; generalized nonexpansive mappings; invariant approximations

Citations:

Zbl 1310.54074
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\textit{M. Abbas} et al., Abstr. Appl. Anal. 2014, Article ID 391952, 5 p. (2014; Zbl 1472.47041)
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References:

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