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Open AccessArticle

Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

1
Department of Mathematics, Shaoxing University, Shaoxing 312000, China
2
Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Korea
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 844; https://doi.org/10.3390/math7090844
Received: 18 July 2019 / Revised: 29 August 2019 / Accepted: 7 September 2019 / Published: 12 September 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms. View Full-Text
Keywords: split common fixed-point problem; strong convergence; demicontractive mapping; viscosity method split common fixed-point problem; strong convergence; demicontractive mapping; viscosity method
MDPI and ACS Style

Wang, Y.; Fang, X.; Kim, T.-H. Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings. Mathematics 2019, 7, 844.

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