JOURNAL BROWSE
Search
Advanced SearchSearch Tips
STRONG CONVERGENCE THEOREMS FOR LOCALLY PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
STRONG CONVERGENCE THEOREMS FOR LOCALLY PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES
Jung, Jong-Soo;
  PDF(new window)
 Abstract
Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowzC, t[0, 1) defined by the equation z
 Keywords
locally pseudo-contractive mapping;locally nonexpansive mapping;fixed points;reflexivity;uniformly Gateaux differentiable norm;
 Language
English
 Cited by
 References
1.
Convexity and Optimization in Banach Spaces, 1978.

2.
Arch. Rational Mech. Anal., 1967. vol.24. pp.82-90

3.
Bull. Amer. Math. Soc., 1967. vol.73. pp.875-882 crossref(new window)

4.
Nonlinear Anal, 1982. vol.6. pp.151-155 crossref(new window)

5.
J. Math. Soc. Japan, 1970. vol.22. pp.443-455 crossref(new window)

6.
Bull. Amer. Math. Soc., 1941. vol.47. pp.313-317 crossref(new window)

7.
Manuscripta Math., 1974. vol.13. pp.365-374 crossref(new window)

8.
Lectures Notes in Math., 1975. vol.485.

9.
Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, 1984.

10.
Pacific J. Math., 1972. vol.40. pp.565-573 crossref(new window)

11.
J. Math. Anal. Appl., 1990. vol.147. pp.330-339 crossref(new window)

12.
Bull. Amer. Math. Soc., 1967. vol.73. pp.957-961 crossref(new window)

13.
Nonlinear Anal., 1998. vol.33. pp.321-329 crossref(new window)

14.
J. Math. Soc. Japan, 1967. vol.19. pp.508-520 crossref(new window)

15.
Manuscripta Math., 1979. vol.30. pp.98-102

16.
Pacific J. Math., 1977. vol.71. pp.89-100 crossref(new window)

17.
Canad. Math. Bull., 1981. vol.24. pp.441-445 crossref(new window)

18.
Trans. Amer. Math. Soc., 1973. vol.179. pp.399-414 crossref(new window)

19.
Proc. Amer. Math. Soc., 1981. vol.81. pp.71-74 crossref(new window)

20.
Houston J. Math., 1990. vol.16. pp.549-557

21.
Bull. London Math. Soc., 1996. vol.28. pp.627-633 crossref(new window)

22.
Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia, 1997. pp.203-212

23.
Proc. Amer. Math. Soc., 2000. vol.128. pp.3411-3419 crossref(new window)

24.
Proc. Amer. Math. Soc., 1995. vol.123. pp.417-423 crossref(new window)

25.
Proc. Amer. Math. Soc., 1995. vol.123. pp.3397-3401 crossref(new window)

26.
J. Funct. Anal., 1980. vol.36. pp.147-168 crossref(new window)

27.
J. Math. Anal. Appl., 1980. vol.75. pp.287-292 crossref(new window)

28.
J. Math. Anal. Appl., 1981. vol.79. pp.113-126 crossref(new window)

29.
Nonlinear Anal., 1998. vol.32. pp.447-454 crossref(new window)

30.
J. Math. Anal. Appl., 1984. vol.104. pp.546-553 crossref(new window)

31.
C. R. Acad. Sci. Paris, Ser. I . Math., 1997. vol.325. pp.151-156 crossref(new window)

32.
Nonlinear Anal., 1995. vol.24. pp.223-228 crossref(new window)

33.
Dissertationes Math., 1971. vol.87. pp.5-33