Existence and structure of the common fixed points based on TVS | Zendy

Issa Mohamadi | Zendy; Shahram Saeidi | Zendy

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Existence and structure of the common fixed points based on TVS

Author(s) -

Issa Mohamadi,

Shahram Saeidi

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1706773m

Subject(s) - mathematics , retract , hausdorff space , fixed point , normed vector space , banach space , regular polygon , commutative property , compact space , topology (electrical circuits) , norm (philosophy) , locally convex topological vector space , strictly convex space , fixed point property , vector space , pure mathematics , discrete mathematics , convex set , topological space , combinatorics , mathematical analysis , convex optimization , geometry , political science , law

In this paper, we investigate the common fixed point property for commutative nonexpansive mappings on $\tau$-compact convex sets in normed and Banach spaces, where $\tau$ 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 $L_1(\mu)$ with a $\sigma$-finite $\mu$ (resp. the James space $J_0$) is a nonempty nonexpansive retract of $C$.

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