×

Three-step iterations for nonlinear accretive operator equations. (English) Zbl 1028.65063

The authors study a three-step iteration scheme of M. A. Noor [J. Math. Anal. Appl. 255, 589-604 (2001; Zbl 0986.49006)] which include known iteration processes like the Krasnosel’skii-Mann iteration. Two convergence theorems are proven.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.

Citations:

Zbl 0986.49006
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ames, W.F., Numerical methods for partial differential equations, (1992), Academic Press New York · Zbl 0219.35007
[2] Browder, F.E., Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. amer. math. soc., 73, 875-882, (1967) · Zbl 0176.45302
[3] Browder, F.E., Nonlinear operators and nonlinear equations of evolutions in Banach spaces, Proc. sympos. pure math., 18, 2, (1976) · Zbl 0176.45301
[4] Chang, S.S., On Chidume’s open questions and approximation solutions of multivalued strongly accretive mapping equations in Banach spaces, J. math. anal. appl., 216, 94-111, (1997) · Zbl 0909.47049
[5] Glowinski, R.; Le Tallec, P., Augemented Lagrangian and operator-splitting methods in nonlinear mechanics, (1989), SIAM Philadelphia · Zbl 0698.73001
[6] Haubruge, S.; Nguyen, V.H.; Strodiot, J.J., Convergence analysis and applications of the glowinski – le tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. optim. theory appl., 97, 3, 645-673, (1998) · Zbl 0908.90209
[7] Huang, Z., Approximating fixed points of φ-hemicontractive mappings by the Ishikawa iteration process with errors in uniformly smooth Banach spaces, Comput. math. appl., 36, 2, 13-21, (1998) · Zbl 0938.47042
[8] Huang, Z., Iterative process with errors for fixed points of multivalued φ-hemicontractive operators in uniformly smooth Banach spaces, Comput. math. appl., 39, 3, 137-145, (2000) · Zbl 0956.47025
[9] Ishikawa, S., Fixed points by a new iteration method, Proc. amer. math. soc., 44, 147-150, (1974) · Zbl 0286.47036
[10] Johnson, G.G., Fixed points by Mean value iteration, Proc. amer. math. soc., 34, 193-194, (1972) · Zbl 0235.47032
[11] Kato, T., Nonlinear semigroup and evolution equations, J. math. soc. Japan, 19, 508-520, (1967) · Zbl 0163.38303
[12] Mann, W.R., Mean value methods in iteration, Proc. amer. math. soc., 4, 506-510, (1953) · Zbl 0050.11603
[13] Noor, M.A., New approximation schemes for general variational inequalities, J. math. anal. appl., 251, 217-229, (2000) · Zbl 0964.49007
[14] Noor, M.A., Three-step iterative algorithms for multivalued quasi variational inclusions, J. math. anal. appl., 255, 589-604, (2001) · Zbl 0986.49006
[15] Noor, M.A., Some predictor – corrector algorithms for multivalued variational inequalities, J. optim. theory appl., 108, 3, 659-670, (2001) · Zbl 0996.47055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.