An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading...

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Bibliographic Details
Published in:Axioms 2021-03, Vol.10 (1), p.1
Main Authors: Abass, Hammed Anuoluwapo, Jolaoso, Lateef Olakunle
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Eigenvalues
Feasibility
fixed point problem
Hilbert space
Iterative algorithms
Iterative methods
Mathematical analysis
multiple-sets split feasibility problem
nonexpansive mappings
Radiation therapy
strictly pseudocontractive mappings
Viscosity
viscossity iterative scheme
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Summary:In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10010001