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Keywords = mixed variational inequalities (MVI)

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11 pages, 257 KiB  
Article
New Iterative Scheme Involving Self-Adaptive Method for Solving Mixed Variational Inequalities
by Aiman Mukheimer, Saleem Ullah, Muhammad Bux, Muhammad Shoaib Arif and Kamaleldin Abodayeh
Axioms 2023, 12(3), 310; https://doi.org/10.3390/axioms12030310 - 20 Mar 2023
Cited by 1 | Viewed by 1642
Abstract
Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point [...] Read more.
Variational inequalities (VI) problems have been generalized and expanded in various ways. The VI principle has become a remarkable study area combining pure and applied research. The study of variational inequality in mathematics is significantly aided by providing an important framework by fixed-point theory. The concept of fixed-point theory can be considered an inherent component of the VI. We consider a mixed variational inequality (MVI) a useful generalization of a classical variational inequality. The projection method is not applicable to solve MVI due to the involvement of the nonlinear term ϕ. MVI is equivalent to fixed-point problems and the resolvent equation techniques. This technique is commonly used in the research on the existence of a solution to the MVI. This paper uses a new self-adaptive method using step size to modify the fixed-point formulation for solving the MVI. We will also provide the convergence of the proposed scheme. Our output could be seen as a significant refinement of the previously known results for MVI. A numerical example is also provided for the implementation of the generated algorithm. Full article
(This article belongs to the Special Issue Fixed Point Theory and Its Related Topics IV)
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