Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

Yaqin Wang, Xiaoli Fang and Tae-Hwa Kim
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Yaqin Wang: Department of Mathematics, Shaoxing University, Shaoxing 312000, China
Xiaoli Fang: Department of Mathematics, Shaoxing University, Shaoxing 312000, China
Tae-Hwa Kim: Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Korea

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: 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.

Keywords: split common fixed-point problem; strong convergence; demicontractive mapping; viscosity method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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