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Iterative method for coupled quasi-solutions of mixed monotone operator equations. (English) Zbl 0763.65041

The authors prove existence theorems for coupled quasi-fixed points for mixed monotone operators and apply their results to the Hammerstein integral equation.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65R20 Numerical methods for integral equations
47J25 Iterative procedures involving nonlinear operators
45G10 Other nonlinear integral equations
47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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References:

[1] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040
[2] Guo, D.; Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 11, 623-632 (1987) · Zbl 0635.47045
[3] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Acadimic Press: Acadimic Press New York · Zbl 0661.47045
[4] Khavanin, M.; Lakshmikantham, V., The method of mixed monotony and first order differential systems, Nonlinear Anal., 10, 873-877 (1986) · Zbl 0611.34016
[5] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S., Monotone Iterative Techniques for Nonlinear Differential Equations (1985), Pitman: Pitman Boston · Zbl 0658.35003
[6] Lakshmikantham, V.; Leela, S.; Vatsala, A. S., Method of quasi-upper and lower solutions in abstract cones, Nonlinear Anal., 6, 833-838 (1982) · Zbl 0497.34047
[7] Pan, X. B., Eigenvectors of non-monotone operator and an iterative method, Computational Mathematics, 2, 131-137 (1988), (in Chinese)
[8] Sun, J., A problem on successive approximations of operator equations, Numer. Math. J. Chinese Univ., 10, 1, 82-87 (1988) · Zbl 0667.65046
[9] Yosida, K., Functional Analysis (1979), Springer-Verlag: Springer-Verlag Berlin · Zbl 0152.32102
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