Let H (1), H (2), H (3) be real Hilbert spaces, let A: H (1) -> H (3), B: H (2) -> H (3) be two bounded linear operators. The split common fixed-point problem (SCFP) is [GRAPHICS] where U: H (1) -> H (1) and ...
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Let H (1), H (2), H (3) be real Hilbert spaces, let A: H (1) -> H (3), B: H (2) -> H (3) be two bounded linear operators. The split common fixed-point problem (SCFP) is [GRAPHICS] where U: H (1) -> H (1) and T: H (2) -> H (2) are two nonlinear operators with nonempty fixed-point sets F(U) = {x is an element of H (1): Ux = x} and F(T) = {x is an element of H (2): Tx = x}. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterativealgorithms with weak convergence for the SCFP (1) of firmly quasi-nonexpansive operators. In this article, we introduce viscosity iterative algorithm and prove the strong convergence of algorithm for the SCFP (1) governed by the directed operators (i.e. firmly quasi-nonexpansive operators). Finally, we provide some applications.
The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable as...
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The aim of this paper is to investigate implicit viscosity iterative algorithm for nonexpansive mappings in the framework of CAT(0) spaces. We prove strong convergence theorems of such algorithm under some suitable assumptions on the sequences of parameters involved therein. We also proved that the presented algorithm is faster than a number of existing iteration processes in literature. Our results extend and improve some recent results of Ahmad et al.[J. Appl. Math. Informatics 35 (5-6)(2017), 423-438] and others.
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