Ishikawa iterative sequence with errors for k-subaccetive operators in arbitrary Banach spaces

• Autorzy: Li Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the iterative solution is studied for equation x+Tx =f with a Lipschitz K-subaccetive operator in arbitrary Banach spaces, some previously results are generalized.

Słowa kluczowe

EN

k-subaccretive operator; nonlinear equation; Ishikawa sequence; Banach space

PL

równania nieliniowe; ciągi Ishikawa; operatory; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 161--168
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Li Y.

• Department of Mathematics Sun Yat-Sen University Guangzhou 510275, P. R. China,

Bibliografia

• [1] F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 875-882.
• [2] R. E. Bruck, The iterative solution of the equation y = x + Tx for a monotone operator T in Hilbert space, Bull. Amer. Math. Soc. 79 (1973), 1258-1262.
• [3] C. E. Chidume, An approximation method for monotone operator, J. Austral. Math. Soc. (series A) 41 (1986), 59-63.
• [4] C. E. Chidume, The iterative solution of the equation f = x + Tx for a monotone operator T in Lp space, J. Math. Anal. Appl. 166 (1986), 531-537.
• [5] C. E. Chidume, H. Zegeye, Approximation of the zeros of m-accretive operator, Nonlinear Anal. 37 (1999), 81-96.
• [6] C. E. Chidume, M. O. Osilike, Nonlinear accretive and pseudo-contractive operator equations in Banach spaces, Nonlinear Anal. 31 (7) (1998), 779-789.
• [7] C. E. Chidume, M. O. Osilike, Iterative solutions of nonlinear accretive operator equations in arbitrary Banach spaces, Nonlinear Anal. 36 (1999), 863-872.
• [8] C. E. Chidume, H. Zegeye, Iterative solution of 0 2 Ax for an m-accretive operator A in certain Banach spaces, J. Math. Anal. Appl. 269 (2002), 421-430.
• [9] W. G. Dotson, An iterative process for nonlinear monotonic nonexpansive operators in Hilbert space, Math. Comp. 32 (1978), 223-225.
• [10] T. Kato, Nonlinear semi-groups and evolutions equations, J. Math. Soc. Japan. 19 (1964), 508-520.
• [11] Liu Lishan, Ishikawa-type and Mann-type iterative process with errors for constructing solutions of nonlinear equations involving m-accretive operators in Banach spaces, Nonlinear Anal. 34 (1998), 307-317.
• [12] R. H. Martin, Jr., A gobal existence theorem for autonomous differential equationsin Banach space, Proc. Amer. Math. Soc. 26 (1970), 307-314.
• [13] S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), 85-92.
• [14] R. T. Rockafellar, Local boundedness of nonlinear monotone operator, Michigan Math J. 16 (1969), 397-407.
• [15] Xu Yuguang, Ishikawa and Mann Iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101.
• [16] Zhu Liang, Iterative solution of nonlinear equations invoiving m-accretive operators in Banach spaces, J. Math. Anal. Appl. 188 (1994), 410-416.