A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-11, Vol.8 (11), p.2039
Main Authors: Jolaoso, Lateef Olakunle, Aphane, Maggie
Format: Article
Language:English
Subjects:
Adaptive algorithms
Algorithms
extragradient method
fixed point
Hilbert space
Inequalities
Linear operators
Lipschitz condition
Mathematical analysis
Mathematics
pseudomonotone
self adaptive stepsize
strong convergence
variational inequalities
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Summary:We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8112039