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2016•arXiv (Cornell University)Open access

The split feasibility and fixed point equality problems for quasi-nonexpansive mappings in Hilbert spaces

L. B. Mohammed, Adem Kılıçman

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Abstract

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert spaces. Furthermore, we study the convergence of the proposed algorithm. At the end, we give numerical example that illustrate our theoretical result. The SFFPEP is a generalization of the split feasibility problem (SFP), split feasibility and fixed point problems (SFFPP) and split equality fixed point problem (SEFPP).

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What this paper is about

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert spaces. Furthermore, we study the convergence of the proposed algorithm. At the end, we give numerical example that illustrate our theoretical result. The SFFPEP is a generalization of the split feasibility problem (SFP), split feasibility and fixed point problems (SFFPP) and split equality fixed point problem (SEFPP).

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Available abstract

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert spaces. Furthermore, we study the convergence of the proposed algorithm. At the end, we give numerical example that illustrate our theoretical result. The SFFPEP is a generalization of the split feasibility problem (SFP), split feasibility and fixed point problems (SFFPP) and split equality fixed point problem (SEFPP).

Key concepts: Fixed point, Hilbert space, Mathematics, Convergence (economics), Generalization, Class (philosophy), Point (geometry), Applied mathematics

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