Three-Step Iterative Algorithms for Multivalued Quasi Variational Inclusions☆

By Muhammad Aslam Noor. 2001

130 citations recorded by the source corpus.

In this paper, we suggest and analyze some new classes of three-step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique. New iterative algorithms include the Ishikawa, Mann, and Noor iterations for solving variational inclusions (inequalities) and optimization problems as special cases. The results obtained in this paper represent an improvement and a significant refinement of previously known results.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/404c72fb0fd336e8b98d14599eb97d7253aab048

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces (2002, methodology): “Our schemes can be viewed as an extension for threestep and two-step iterative schemes of Glowinski and Le Tallec [4], Noor [11–13], and Ishikawa [8].”
Three-step iterations for nonlinear accretive operator equations (2002, methodology): “For the applications of the splitting and decomposition methods, see [1,5,6,13–15] and the references therein.”
New Trends in General Variational Inequalities (2020, background): “See [6, 7, 8, 9, 10, 17, 18, 24, 36, 37, 39, 42, 43, 44, 49, 55, 63, 68, 71, 79, 82, 83, 90, 92, 95, 100, 101, 102, 103, 104, 106, 107, 110, 111, 112, 113, 114, 116, 117, 119, 120, 133, 134, 135, 137, 138, 143, 144, 145, 146, 150, 152, 153, 160] and the references therein.”
Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces (2008, methodology): “The three-step schemes are natural generalization of the splitting methods to solve partial differential equations (inclusions); for details, see, Noor [14–16].”
Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings (2006, methodology): “Fixed-point iteration processes for asymptotically nonexpansive mapping in Banach spaces including Mann and Ishikawa iterations processes have been studied extensively by many authors; see [1–19,22,23].”