Approximation of fixed points

of strongly pseudocontractive maps

without Lipschitz assumption

Authors:
Zhou Haiyun and Jia Yuting

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1705-1709

MSC (1991):
Primary 47H17

MathSciNet review:
1389522

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Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper, the following result is shown: Let be a real Banach space with a uniformly convex dual , and let be a nonempty closed convex and bounded subset of . Assume that is a continuous strong pseudocontraction. Let and be two real sequences satisfying (i) for all ; (ii) ; and (iii) as Then the Ishikawa iterative sequence generated by

converges strongly to the unique fixed point of .

**1.**Felix E. Browder,*Nonlinear operators and nonlinear equations of evolution in Banach spaces*, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R. I., 1976, pp. 1–308. MR**0405188****2.**Viorel Barbu,*Nonlinear semigroups and differential equations in Banach spaces*, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR**0390843****3.**J. Bogin, On strict pseudo-contractions and a fixed point theorem, Technion Preprint MT-29, Haifa, 1974.**4.**C. E. Chidume,*Approximation of fixed points of strongly pseudocontractive mappings*, Proc. Amer. Math. Soc.**120**(1994), no. 2, 545–551. MR**1165050**, 10.1090/S0002-9939-1994-1165050-6**5.**Klaus Deimling,*Zeros of accretive operators*, Manuscripta Math.**13**(1974), 365–374. MR**0350538**

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Additional Information

**Zhou Haiyun**

Affiliation:
Department of Mathematics, Hebei Teachers University, Shijiazhuang 050016, People’s Republic of China

**Jia Yuting**

Affiliation:
Department of Mathematics, Hebei Teachers University, Shijiazhuang 050016, People’s Republic of China

DOI:
http://dx.doi.org/10.1090/S0002-9939-97-03850-1

Keywords:
The Ishikawa iteration,
strong pseudocontraction,
strictly convex Banach space

Received by editor(s):
December 5, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society