Approximation of solutions of generalized equations of Hammerstein type

Computers and Mathematics with Applications

Volumn 63, Issue 5, 2012, Pages 966-974

  Chidume, C E ^a   Shehu, Y ^a  

^a AFRICAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Nigeria)

Author keywords

Equations of Hammerstein type; Hilbert spaces; Monotone operators; Strong convergence

Indexed keywords

VECTOR SPACES;

EXPLICIT ITERATIVE; GENERALIZED EQUATIONS; HAMMERSTEIN EQUATIONS; HAMMERSTEIN TYPE; MONOTONE MAPPINGS; MONOTONE OPERATORS; STRONG CONVERGENCE;

HILBERT SPACES;

EID: 84865653893     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.12.001     Document Type: Article

References (32)

1. H.K. Xu, Inequality in Banach spaces with applications, Nonlinear Anal. 16 (1991) 1127-1138
2. Z.B. Xu, G.F. Roach, Characteristic inequalities of 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 19 (1967) 508-520
5. V. Berinde, Iterative Approximation of Fixed Points, in: Springer-Verlag Series: Lecture Notes in Mathematics, vol. 1912, ISBN: 978-3-540-72233-5, 2007
6. V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002
7. C.E. Chidume, Geometric Properties of Banach Spaces and Nonlinear Iterations, in: Springer-Verlag Series: Lecture Notes in Mathematics, vol. 1965, ISBN: 978-1-84882-189-7, 2009, XVII, p. 326
8. I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer Academic, Dordrecht, 1990
9. S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 183 (1994) 118-120
10. A. Hammerstein, Nichtlineare integralgleichungen nebst anwendungen, Acta Math. 54 (1930) 117-176
11. D. Pascali, S. Sburlan, Nonlinear Mappings of Monotone Type, Editura Academiae, Bucharest, Romania, 1978
12. V. Dolezale, Monotone Operators and its Applications in Automation and Network Theory, in: Studies in Automation and Control, Elsevier Science Publ., New York, 1979
13. H. Brézis, F.E. Browder, Some new results about Hammerstein equations, Bull. Amer. Math. Soc. 80 (1974) 567-572
14. H. Brézis, F.E. Browder, Existence theorems for nonlinear integral equations of Hammerstein type, Bull. Amer. Math. Soc. 81 (1975) 73-78
15. H. Brézis, F.E. Browder, Nonlinear integral equations and system of Hammerstein type, Adv. Math. 18 (1975) 115-147
16. F.E. Browder, D.G. Figueiredo, P. Gupta, Maximal monotone operators and a nonlinear integral equations of Hammerstein type, Bull. Amer. Math. Soc. 76 (1970) 700-705
17. F.E. Browder, P. Gupta, Monotone operators and nonlinear integral equations of Hammerstein type, Bull. Amer. Math. Soc. 75 (1969) 1347-1353
18. R.Sh. Chepanovich, Nonlinear Hammerstein equations and fixed points, Publ. Inst. Math. (Beograd) (NS) 35 (1984) 119-123
19. D.G. De Figueiredo, C.P. Gupta, On the variational methods for the existence of solutions to nonlinear equations of Hammerstein type, Bull. Amer. Math. Soc. 40 (1973) 470-476
20. W.R. Mann, Mean value methods in iterations, Bull. Amer. Math. Soc. 4 (1953) 506-510
21. C.E. Chidume, N. Djitte, Approximation of solutions of Hammerstein equations with bounded strongly accretive nonlinear operators, Nonlinear Anal. 70 (2009) 4071-4078
22. C.E. Chidume, N. Djitte, Iterative approximation of solutions of nonlinear equations of Hammerstein type, Nonlinear Anal. 70 (2009) 4086-4092
23. G. Infante, P. Pietramala, Existence and multiplicity of non-negative solutions for systems of pertubed Hammerstein integral equations, Nonlinear Anal. 71 (2009) 1301-1310
24. Z. Yang, D. O'Regan, Positive solvability of systems of nonlinear Hammerstein integral equations, J. Math. Anal. Appl. 311 (2005) 600-614 (Pubitemid 41350224)
25. C.E. Chidume, E.U. Ofoedu, Solution of nonlinear integral equations of Hammerstein type, Nonlinear Anal. 74 (2011) 4293-4299
26. C.P. Gupta, Nonlinear equations of Urysohn's type in a Banach space, Comment. Math. Univ. Carolin. 16 (1975) 377-386
27. C.P. Gupta, On a class of nonlinear integral equations of Urysohn's type, J. Math. Anal. Appl. 58 (1977) 344-360
28. F.E. Browder, Nonlinear functional analysis and nonlinear integral equations of Hammerstein and Urysohn type, in: Contributions to Nonlinear Functional Analysis, Academic Press, 1971, pp. 425-500
29. M. Joshi, Existence theorem for a generalized Hammerstein type equation, Comment. Math. Univ. Carolin. 15 (1974) 283-291
30. H.K. Xu, Iterative algorithm for nonlinear operators, J. Lond. Math. Soc. 66 (2) (2002) 1-17
31. S. Shioji, W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 125 (1997) 3641-3645 (Pubitemid 127744357)
32. S.S. Chang, Y.J. Cho, H. Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, Inc., Huntington, NY, 2002.