Halpern–Ishikawa type iterative schemes for approximating fixed points of multi-valued non-self mappings
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Abstract Let C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$ T : C → C B ( H ) be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$ T : C → P r o x ( H ) is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.
2020 ◽
Vol 16
(01)
◽
pp. 89-103
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2010 ◽
Vol 2010
◽
pp. 1-13
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