Ishikawa-type and Mann-type iterative processes with errors for constructing solutions of nonlinear equations involving m-accretive operators in Banach spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 34, Issue 2, 1998, Pages 307-317

  Lishan, Liu ^a  

^a QUFU NORMAL UNIVERSITY   (China)

Author keywords

Banach space; m accretive operators; Mann and Ishikawa type iterative processes with errors

Indexed keywords

CONFORMAL MAPPING; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; SET THEORY; STATE SPACE METHODS; THEOREM PROVING;

BANACH SPACES; HILBERT SPACE; MANN TYPE ITERATIVE PROCESSES;

NONLINEAR EQUATIONS;

EID: 0032188316     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00579-8     Document Type: Article

References (33)

1. H.K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991) 1127-1138.
2. Z.B. Xu, G.F. Roach, Characteristics inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991) 189-210.
3. F.E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967) 875-882.
4. T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan. 18/19 (1967) 508-520.
5. R.H. Martin, A global existence theorem for autonomous differential equations in Banach spaces, Proc. Amer. Math. Soc. 26 (1970) 307-314.
6. F.E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math. 18, 1976, Part 2.
7. E. Zeidler, Nonlinear Functional Analysis and Its Applications, Part II. Monotone Operators. Springer-Verlag, New York, 1985.
8. R.E. Bruck, The iterative solution of the equation f ∈ x + Tx for a monotone operator T in Hubert space, Bull. Amer. Math. Soc. 79 (1973) 1258-1262.
9. C.E. Chidume, The iterative solution of the equations y ∈ x + Tx for a monotone operator T in Lp spaces, J. Math. Anal. Appl. 116 (1986) 531-537.
10. C.E. Chidume, An approximation method for monotone Lipschitzian operators in Hilbert spaces, J. Austral. Math. Soc. Ser. A, 41 (1986) 59-63.
11. C.E. Chidume, Iterative solution of nonlinear equations of the monotone type in Banach spaces, Bull. Austral. Math. Soc. 42 (1990) 21-31.
12. C.E. Chidume, M.O. Osilike, Approximation methods for nonlinear operator equations of the m-accretive type, J. Math. Anal. Appl. 189 (1995) 225-239.
13. W.G. Dotson, An iterative process for nonlinear monotonie nonexpansive operators in Hilbert space, Math. Comp. 32 (1978) 223-225.
14. L. Zhu, Iterative solution of nonlinear equations involving m-accretive operators in Banach spaces, J. Math. Anal. Appl. 188 (1994) 410-416.
15. L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125.
16. W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953) 506-510.
17. S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974) 147-150.
18. S. Reich, Constructing zeros of accretive operators, I, II. Applicable Analysis. 8 (1979) 349-352; 9 (1979) 159-163
19. S. Reich, Constructing zeros of accretive operators, I, II. Applicable Analysis. 8 (1979) 349-352; 9 (1979) 159-163
20. J. Gwinner, On the convergence of some iteration processes in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 81 (1978) 29-35.
21. L.S. Liu, Fixed points of local strictly pseudo-contractive mappings using Mann and Ishikawa iteration with errors, Indian J. Pure Appl. Math. 26 (1995) 649-659.
22. L.S. Liu, Mann iteration processes for constructing a solution of strongly monotone operator equations, J. Enginee. Math. 10(4) (1993) 117-121, (Chinese).
23. B.E. Rhoades, Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976) 741-750.
24. B.E. Rhoades, Some fixed point iteration procedures, Int. J. Math. Sci. 14 (1991) 1-16.
25. K.K. Tan, H.K. Xu, Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces, J. Math. Anal. Appl. 178 (1993) 9-21.
26. Z.Y. You, Pseudo-monotonic sequence and convergence of convex combined iteration with errors, Numer. Math. J. Chinese Univ. 4 (1983) 336-341, (Chinese).
27. J. Borwein, S. Reich, I. Shafrir Krasnoselski - Mann iterations in normed spaces, Canad. Math. Bull. 35 (1992) 21-28.
28. R.E. Bruck, S. Reich, A general convergence principle in nonlinear functional analysis, Nonlinear Anal. 4 (1980) 939-950.
29. O. Nevanlinna and S. Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel. J. Math. 32 (1979) 44-58.
30. S. Reich, Constructive techniques for accretive and monotone operators, In Applied Nonlinear Analysis, Ed. V. Lakshmikantham, Academic Press, New York, 1979, pp. 335-345.
31. S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292.
32. B. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976.
33. S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978) 85-92.