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ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS
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 Title & Authors
ON THE ON THE CONVERGENCE BETWEEN THE MANN ITERATION AND ISHIKAWA ITERATION FOR THE GENERALIZED LIPSCHITZIAN AND Φ-STRONGLY PSEUDOCONTRACTIVE MAPPINGS
Xue, Zhiqun;
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 Abstract
In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and -strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].
 Keywords
Ishikawa iteration;Mann iteration;-strongly pseudocontractive maps;generalized Lipschitz maps;uniformly smooth Banach spaces;
 Language
English
 Cited by
 References
1.
V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania, Bucharest; Noordhoff International Publishing, Leiden, 1976

2.
J. Bogin, On Strict Pseudo-Contractions and a Fixed Point Theorem, Technion Preprint MT-29, Haifa, 1974

3.
F. 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), pp. 1-308. Amer. Math. Soc., Providence, R. I., 1976

4.
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985

5.
T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520 crossref(new window)

6.
B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators, Int. J. Math. Math. Sci. (2003), no. 42, 2645-2651 crossref(new window)

7.
B. E. Rhoades and S. M. Soltuz, On the equivalence of Mann and Ishikawa iteration methods, Int. J. Math. Math. Sci. (2003), no. 7, 451-459 crossref(new window)

8.
X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 113 (1991), no. 3, 727-731