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Iterative approximation of fixed points for $\phi$-hemicontractive operators in Banach spaces

Shin Min Kang|Zeqing Liu|Zhefu An|Yanjuan Li
대한수학회 (The Korean Mathematical Society)|2004.01|대한수학회논문집 (Communications of the KMS)|제19권 제1호|pp. 63-74

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주제분류수학

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Abstract

Suppose that X is a real Banach space, K is anon-em-pty closed convex subset of X and T:Kto K is auniformly continuous phi-hemicontractive operator or aLipschitz phi -hemicontractive operator. In this paper we provethat under certain conditions the three-step iteration methodswith errors converge strongly to the unique fixed point of T.Our results extend the corresponding results of Chang [1], Changet al. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10],Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu[17].

참고문헌 (17)

  1. "Some problems and results in the study of nonlinear analysis", 30, pp.4197~4208 (1997)
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  3. "C. E. Chidume\paper Iterative approximation offixed points of Lipschitz strictly pseudocontractive mappings\jourProc. Amer. Math. Soc. \vol 99\yr 1987\pages 283--288"
  4. "An iterative process for nonlinearLipschitzian strongly accretive mappings in $L_p$ spaces\jour J.Math. Anal. Appl. \vol 151\yr 1990\pages 453--461"
  5. "Approximation of fixed points ofstrongly pseudo-contractive mappings\jour Proc. Amer. Math.Soc.\vol 120\yr 1994 \pages 545--551"
  6. "Iterative solution of nonlinear equations with strongly accretive operators", 192, pp.502~518 (1995)
  7. "Iterative solution of nonlinearequations in smooth Banach spaces", 26, pp.1823~1824 (1996)
  8. "Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces", 15
  9. "Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings", 192, pp.727~741 (1995)
  10. "An iterative process for nonlinearLipschitz and strongly accretive mappings in uniformly convex anduniformly smooth Banach spaces" (1993)
  11. "Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces", 194, pp.114~125 (1995)
  12. "Convergence theorems for $\phi$-strongly accretive and $\phi$-hemicontractive operators", 253, pp.35~49 (2001)
  13. "Iterative approximation of fixedpoints for $\phi$-hemi\-con\-tra\-c\-tive operators in arbitraryBanach spaces", 67, pp.821~831 (2001)
  14. "Iterative solution ofnonlinear equations of the $\phi$-strongly accretive type", 200, pp.259~271 (1996)
  15. "Iterative solution of nonlinear$\phi$-strongly accretive operator equations in arbitrary Banach spaces", 36, pp.1~9 (1999)
  16. "K. K. Tan and H. K. Xu\paper Iterative solutionsto nonlinear equations of strongly accretive operators in Banachspaces\jour J. Math. Anal. Appl.\vol 178\yr 1993\pages 9--21"
  17. "Approximating fixed points ofnonexpansive mappings by the Ishikawa iteration process jour J.Math. Anal. Appl.\vol 178\yr 1993\pages 301--308"

관련 논문AI추천

Iterative approximation of fixed points for strongly pseudo-contractive mappingsBhavana Deshpande, Sushil Sharma대한수학회 · 대한수학회보2002 · 제39권 제1호Almost stability of Ishikawa iterative schemes with errors for $\phi$-strongly quasi-accretive and $\phi$-hemicontractive operatorsJong Kyu Kim, Shin Min Kang, Zeqing Liu대한수학회 · 대한수학회논문집2004 · 제19권 제2호Necessary and sufficient conditions for convergence of Ishikawa iterative schemes with errors to $\phi$-hemicontractive mappingsJong Kyu Kim, Shin Min Kang, Zeqing Liu대한수학회 · 대한수학회논문집2003 · 제18권 제2호Convergence and Almost Stability of Ishikawa Iteration Method with Errors for Strictly Hemi-Contractive Operators in Banach Spaces강신민, 엄정석, Zeqing Liu한국수학교육학회 · 이론수학과 교직수학2004 · 제11권 제4호Almost stability of the Mann iteration method with errors for strictly hemi-contractive operators in smooth Banach spaces강신민, 심수학, Z. Liu대한수학회 · 대한수학회지2003 · 제40권 제1호Iterative Approximations of Zeroes for Accretive Operators in Banach Spaces김종규, 조열제, Haiyun Zhou대한수학회 · 대한수학회논문집2006 · 제21권 제2호

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