An inertia-based algorithm for pseudomonotone variational inequality and fixed point problems in real Hilbert space

Volume 15, Issue 3, pp 209--224 http://dx.doi.org/10.22436/jnsa.015.03.04

Publication Date: April 13, 2022 Submission Date: January 22, 2021 Revision Date: February 27, 2021 Accteptance Date: January 01, 2022

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Authors

J. N. Ezeora - Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria. R. C. Ogbonna - Department of Computer Science and Mathematics, Evangel University, Aka-eze, Aka-eze. F. E. Bazuaye - Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria.

Abstract

The aim of this work is to study a pseudomonotone variational inequality and a fixed point problem involving pseudocontractive mappings in real Hilbert spaces. We introduce an inertia-based iterative algorithm for finding a common solution to this problem. The strong convergence of the proposed algorithm is proved. Finally, numerical examples are provided and also meaningful comparisons of these results with those in [Y. Yao, M. Postolache, J. C. Yao, Mathematics, \(\textbf{7}\) (2019), 14 pages], proving that at our proposed numerical schemes are more efficient.

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Keywords

• Pseudomonotone variational inequality
• pseudocontractive mapping
• fixed point problem
• Hilbert space

MSC

•  47H09
•  47H10
•  49M05
•  54H25

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