A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems

Vasile Berinde ()
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Vasile Berinde: Department of Mathematics and Computer Science, North University Centre at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430072 Baia Mare, Romania

Mathematics, 2024, vol. 12, issue 20, 1-17

Abstract: This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated by this method to the common solution for the fixed point problem and the variational inequality problem. In order to illustrate the feasibility of the hypotheses and the superiority of our theoretical results over the existing literature, an example is also presented.

Keywords: Hilbert space; nonexpansive mapping; strictly pseudocontractive mapping; fixed point; common fixed point; variational inequality; implicit algorithm; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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