Stability of a new iteration method for strongly pseudocontractive mappings

• Autorzy: Stević S.
• Języki publikacji: EN

Abstrakty

EN

In this note we prove that a recently introduced iteration procedure is almost stable with respect to strong pseudocontractions in real uniformly Banach spaces.

Słowa kluczowe

EN

iteration method; difference inequality; strongly pseudocontractive; almost stable; duality mapping; Banach space

PL

iteracja; nierówności różniczkowe; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 404--412
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Stević S.

• Matematički Fakultet, Studentski Trg 16, 11000 Beograd, Serbia, Yugoslavia

Bibliografia

• [1] S. S. Chang, On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces, J. Math. Anal. Appl. 216 (1997), 94-111.
• [2] C. E. Chidume, Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings, Proc. Amer. Math. Soc. 99 (1987), 283-288.
• [3] C. E. Chidume, An iterative proces for nonlinear Lipschitzian strongly accretive mappings in Lp spaces, J. Math. Anal. Appl. 151 (1990), 453-461.
• [4] C. E. Chidume, Approximation of fixed points of strongly pseudocontractive mappings, Proc. Amer. Math. Soc. 120 (1994), 545-551.
• [5] L. Deng and X. P. Ding, Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces, Nonlinear Anal. TMA 24 (1995), 981-987.
• [6] J. C. Dunn, Iterative construction of fixed points for multivalued operators of the monotone type, J. Funct. Anal. 27 (1978), 38-50.
• [7] A. M. Harder and T. L. Hicks, A stable iteration procedure for nonexpansive mappings, Math. Japon. 33 (1988), 687-692.
• [8] A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japon. 33 (1988), 693-706.
• [9] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150.
• [10] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 18/19 (1967), 508-520.
• [11] L. Liu, Approximation of fixed points of a strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 125 (5) (1997), 1363-1366.
• [12] L.-S. Liu, Fixed points of local strictly pseudo-contractive mappings using Mann and Ishikawa iteration with errors, Indian J. Pure. Appl. Math. 26 (7) (1995), 649-659.
• [13] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.
• [14] M. O. Osilike, Stability results for the Ishikawa fixed point iteration procedures, Indian J. Pure Appl. Math. 26 (1995), 937-945.
• [15] M. O. Osilike, Stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (3), (1996), 259-271.
• [16] M. O. Osilike, Stable iteration procedures for nonlinear pseudocontractive and accretive operators in arbitrary Banach spaces, Indian J. Pure Appl. Math. 28 (8), (1997), 1017-1029.
• [17] M. O. Osilike, Stability of the Mann and Ishikawa iteration procedures for φ-strong pseudocontractions and nonlinear equations of the φ-stongly accretive type, J. Math. Anal. Appl. 227 (1998), 319-334.
• [18] M. O. Osilike and A. Udomene, Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mapping, Indian J. Pure Appl. Math. 30 (12) (1999), 1229-34.
• [19] W. V. Petryshin, A characterization of strict convexity of Banach spaces and other uses of duality mappings, J. Funct. Anal. 6 (1970), 282-291.
• [20] L. Qihou, A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mapping, J. Math. Anal. Appl. 146 (1990), 301-305.
• [21] S. Reich, An iterative procedure for construction zeros of accretive sets in Banach spaces, Nonlinear Anal. TMA 2 (1978), 85-92.
• [22] S. Stević, On stability results for a new approximating fixed points iteration process, Demonstratio Math. 34 (4) (2001), 873-880.
• [23] S. Stević, Approximating fixed points of nonexpansive mappings by a new iteration method, Far East J. Math. Sci. (to appear).
• [24] K. K. Tan and H. K. Xu, Iterative solution to nonlinear equations and strongly accretive operators in Banach spaces, J. Math. Anal. Appl. 178 (1993), 9-21.
• [25] X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 113 (1991), 727-731.
• [26] Z. B. Xu and G. F. Roach, Characteristics inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991), 189-210.
• [27] H. Zhou and Y. Jia, Approximation of fixed points of strongly pseudo-contractive maps without Lipschitz assumption, Proc. Amer. Math. Soc. 125 (6) (1997), 1705-1709.