Common fixed point property through analysis of retractions

Saeidi, Shahram

doi:10.1007/s11784-014-0196-x

Cited by 3 publications

(2 citation statements)

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“…Nonexpansive retract plays an important role in the study of the structure of fixed point sets of nonexpansive mappings. We refer the reader to [6][7][8]15,[24][25][26] for more information concerning nonexpansive retracts. It is known that the fixed point set of a Q-nonexpansive mapping is not necessarily convex.…”

Section: Nonexpansive Retractionsmentioning

confidence: 99%

Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces

Bakhande

Saeidi

2019

J. Fixed Point Theory Appl.

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In this paper, we will be concerned with a problem raised by Lau (Fixed Point Theory Appl, 2010) for the existence of common fixed points for a right reversible semitopological semigroup S acting asymptotically nonexpansive on a nonempty compact convex set in the framework of locally convex spaces. We give answers to this problem under the left amenability of ARUC(S) and LMC(S) and then study the existence of Q-nonexpansive retractions in the pointwise closure of S using a new method.

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Section: Nonexpansive Retractionsmentioning

confidence: 99%

Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces

Bakhande

Saeidi

2019

J. Fixed Point Theory Appl.

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“…Bruck [4] showed that a Banach space E having the weak fpp has the weak fpp for commutative semigroups. We refer to [23] for a simple proof to a more general version of Bruck's result. For a dual Banach space E satisfying the weak* fpp, it is still unknown whether E has the weak* fpp for commutative semigroups.…”

Section: Introductionmentioning

confidence: 99%

Existence and structure of the common fixed points based on TVS

Mohamadi¹,

Saeidi²

2017

Filomat

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In this paper, we investigate the common fixed point property for commutative nonexpansive mappings on τ-compact convex sets in normed and Banach spaces, where τ is a Hausdorff topological vector space topology that is weaker than the norm topology. As a consequence of our main results, we obtain that the set of common fixed points of any commutative family of nonexpansive self-mappings of a nonempty clm-compact (resp. weak* compact) convex subset C of L 1 (µ) with a σ-finite µ (resp. the James space J 0 ) is a nonempty nonexpansive retract of C.

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