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Some Stability Results for Coincidence Point Iterative Algorithms with Three Mappings

강미광|김승현
한국수학교육학회|2020.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제27권 제1호|pp. 61-70|DOI https://doi.org/10.7468/jksmeb.2020.27.1.61

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참고문헌

키워드

stabilitycoincidence pointiterative algorithm.
주제분류수학

초록

In this paper, we introduce a new concept of stability of coincidence iterative algorithm for three mappings and derive a new three-step Jungck-type iterative algorithm. And, we prove a stability result and a strong convergence result for the Jungck-type algorithm using the MJ -contractive condition. Our results extend and unify the corresponding ones in [3, 6, 7, 13].

Abstract

In this paper, we introduce a new concept of stability of coincidence iterative algorithm for three mappings and derive a new three-step Jungck-type iterative algorithm. And, we prove a stability result and a strong convergence result for the Jungck-type algorithm using the MJ -contractive condition. Our results extend and unify the corresponding ones in [3, 6, 7, 13].

참고문헌 (14)

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  2. S. Ishikawa, "Fixed point by a new iteration method", Proc. Amer. Math. Soc., 44(1), pp.147~150 (1974)
  3. G. Jungck, "Commuting mapping and fixed points", Amer. Math. Monthly, 83(4), pp.261~263 (1976)
  4. W. R. Mann, "Mean value methods in itewration", Proc. Amer. Math. Soc, 4, pp.506~510 (1953)
  5. M. A. Noor, "Three-stpe iterations for nonlinear accretive operator equations", J. Math. Anal. Appl., 274, pp.59~68 (2002)
  6. M.O. Olatinwo, "Some stability and convergence results for Picard, Mann, Ishikawa and Jungck type iterative algorithms for Akram-Zafar-Siddiqui type contraction mappings", Nonlinear Anal. Forum, 21(1), pp.65~75 (2016)
  7. M.O. Olatinwo, "Some stability and strong convergence results for the Jungck-Ishikawa iteration process", Creat. Math. Inform., 17, pp.33~42 (2008)
  8. M.O. Osilike, "Some stability results for fixed point iteration procedures", J. Nigerian Math. Soc., 14, pp.15 (1995), 17~29
  9. M.O. Osilike, "Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings", Indian J. Pure Appl. Math., 30(12), pp.1229~1234 (1999)
  10. L. Qihou, "A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings", J. Math. Anal. Appl., 146, pp.301~305 (1990)
  11. B.E. Rhoades, "Fixed point theorems and stability results for fixed point iteration pro-cedures", Indian J. Pure Appl. Math., 21(1), pp.1~9 (1990)
  12. B.E. Rhoades, "Fixed point theorems and stability results for fixed point iteration pro-cedures II", Indian J. Pure Appl. Math., 24(11), pp.691~703 (1993)
  13. S.L. Singh, "Stability of Jungck-type iterative procedures", Int. J. Math. Math. Sci., 2005(19), pp.3035~3043 (2005)
  14. V. Verinde, "On the stability of some fixed point procedures", Bul. Stiint. Univ. Baia Mare, Ser. B, Mathematica-Informatica, 18(1), pp.7~14 (2002)

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