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A new method for split common fixed-point problem without priori knowledge of operator norms

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Abstract

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a linear transformation belongs to another fixed-point set. In this paper, we propose a new algorithm for the split common fixed-point problem that does not need any priori information of the operator norm. Under standard assumptions, we establish a weak convergence theorem of the proposed algorithm.

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Acknowledgements

The author would like to express his sincere appreciation to the referees for their valuable and constructive comments of the manuscript. This work was supported by Program for Science and Technology Innovation Talents in the Universities of Henan Province (Grant No. 15HASTIT013) and Innovation Scientists and Technicians Troop Construction Projects of Henan Province (Grant No. CXTD20150027).

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Authors and Affiliations

  1. Department of Mathematics, Luoyang Normal University, Luoyang, 471022, China

    Fenghui Wang

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  1. Fenghui Wang
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Correspondence to Fenghui Wang.

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Wang, F. A new method for split common fixed-point problem without priori knowledge of operator norms. J. Fixed Point Theory Appl. 19, 2427–2436 (2017). https://doi.org/10.1007/s11784-017-0434-0

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