Characterization of weak fixed point property for new class of set-valued nonexpansive mappings

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Hajisharifi Hamid Reza

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ISSN: 2588-4824

Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:18 Page(s): 95-104

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Title

Characterization of weak fixed point property for new class of set-valued nonexpansive mappings

Author(s)

Hajisharifi Hamid Reza | Issue Writer Certificate

Keywords

fixed point

Suzuki type mappings

Asymptotic radius

Asymptotic center

D-type mappings

Abstract

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-continuous L-type mappings and upper semi-continuous quasi-nonexpansive mappings. We study relationships between MD-type mappings and some other set-valued generalization of nonexpansive mappings. In the sequel we show that if E is a nonempty, weakly compact and convex subset of a Banach space (X, ‖ . ‖ ) for which every D-type self-mapping on E has a fixed point, then every MD-type self-mapping on E has a fixed point. This result gives a partial affirmative answer to an open problem of Rich. Moreover, we establish some fixed theorems for MD-type mappings which generalize some well-known results in the literature.

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APA: Copy

Hajisharifi, Hamid Reza. (2019). Characterization of weak fixed point property for new class of set-valued nonexpansive mappings. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(18 ), 95-104. SID. https://sid.ir/paper/731942/en

Vancouver: Copy

Hajisharifi Hamid Reza. Characterization of weak fixed point property for new class of set-valued nonexpansive mappings. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(18 ):95-104. Available from: https://sid.ir/paper/731942/en

IEEE: Copy

Hamid Reza Hajisharifi, “Characterization of weak fixed point property for new class of set-valued nonexpansive mappings,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 18 , pp. 95–104, 2019, [Online]. Available: https://sid.ir/paper/731942/en

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