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Some convergence problem of iterative sequences for accretive and pseudo-contractive type mapping in banach spaces

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Abstract

Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.

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References

  1. Browder F E. Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J].Bull Amer Math Soc, 1967,73:875–882.

    Article  MATH  MathSciNet  Google Scholar 

  2. Deimling K. Zeros of accretive mapping[J].Manuscripta Math, 1974,13:365–374.

    Article  MATH  MathSciNet  Google Scholar 

  3. Martin R H. A global existence theorem for autonomous differential equations in Banach spaces[J].Proc Amer Math Soc, 1970,26:307–314.

    Article  MATH  MathSciNet  Google Scholar 

  4. CHANG Shih-sen. On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces[J].J Math Anal Appl, 1997,216:94–111.

    Article  MathSciNet  Google Scholar 

  5. CHANG Shih-sen. Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA, 1997,30:4197–4208.

    Article  Google Scholar 

  6. CHANG Shih-sen, Cho Y J, Lee B S, et al. Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces[J].J Math Anal Appl, 1998,224:149–165.

    Article  MathSciNet  Google Scholar 

  7. Chidume C E. Steepest descent approximations for accretive operator equations[J].Nonlinear Anal, TMA, 1996,26:299–311.

    Article  MATH  MathSciNet  Google Scholar 

  8. Chidume C E, Osilike M O. Nonlinear accretive and pseudo-contractive operator equations in Banach spaces[J].Nonlinear Anal, TMA, 1998,31:779–789.

    Article  MATH  MathSciNet  Google Scholar 

  9. Chidume C E. Iterative solutions of nonlinear equations with strongly accretive operators[J].J Math Anal Appl, 1995,192:502–518.

    Article  MATH  MathSciNet  Google Scholar 

  10. Chidume C E. Global iteration schemes for strongly pseudo-contractive maps[J].Proc Amer Math Soc, 1998,126(9):2614–2649.

    Article  MathSciNet  Google Scholar 

  11. Deng L, Ding X P. Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces[J].Nonlinear Anal, TMA, 1995,24:981–987.

    Article  MATH  MathSciNet  Google Scholar 

  12. Liu L W. Approximation of fixed points of a strongly pseudo-contractive mappings[J].Proc Amer Math Soc, 1997,125:1363–1366.

    Article  MATH  MathSciNet  Google Scholar 

  13. Tan K K, Xu H K. Iterative solution to nonlinear equations and strongly accretive operators in Banach spaces[J].J Math Anal Appl, 1993,178:9–21.

    Article  MATH  MathSciNet  Google Scholar 

  14. Xu Z B, Roach G F. A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations[J].J Math Anal Appl, 1992,167:340–354.

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhou H Y, Jia Y T. Approximation of fixed points of strongly pseudo-contractive maps without Lipschitz assumption[J].Proc Amer Math Soc, 1997,125:1705–1709.

    Article  MATH  MathSciNet  Google Scholar 

  16. Fitzpatrick P M, Hess P, Kato T. Local boundedness of monotone type operators[J].Proc Japan Acad, 1972,48:275–277.

    Article  MATH  MathSciNet  Google Scholar 

  17. Kato T. Nonlinear semigroups and evolution equations[J].J Math Soc Japan, 1967,19:508–520.

    Article  MATH  MathSciNet  Google Scholar 

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Contributed by Zhang Shi-sheng

Biography: Zhang Shi-zheng (1934-)

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Shi-sheng, Z. Some convergence problem of iterative sequences for accretive and pseudo-contractive type mapping in banach spaces. Appl Math Mech 23, 394–408 (2002). https://doi.org/10.1007/BF02436208

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  • DOI: https://doi.org/10.1007/BF02436208

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