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Information Journal Paper

Title

ITERATIVE SCHEME BASED ON BOUNDARY POINT METHOD FOR COMMON FIXED POINT OF STRONGLY NONEXPANSIVE SEQUENCES

Author(s)

 ZHU WENLONG | LING SHUAI

Pages

  719-730

Abstract

 Let C be a nonempty closed convex subset of a real Hilbert space H. Let {Sn} and {Tn} be sequences of nonexpansive self-mappings of C, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process xn+1=bnxn+(1-bn) Sn (anu+(1-an) Tnxn) for finding the common fixed point of {Sn} and {Tn}, where uÎC is an arbitrarily (but fixed) element in C, x0ÎC arbitrarily, {an} and {bn} are sequences in [0; 1]. But in the case where uÏC, the iterative scheme above becomes invalid because xn may not belong to C. To overcome this weakness, a new iterative scheme based on the thought of BOUNDARY POINT METHOD is proposed and the STRONG CONVERGENCE theorem is proved. As a special case, we can find the MINIMUM-NORM COMMON FIXED POINT of {Sn} and {Tn} whether 0ÎC or 0ÏC.

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    • Cite

    APA: Copy

    ZHU, WENLONG, & LING, SHUAI. (2016). ITERATIVE SCHEME BASED ON BOUNDARY POINT METHOD FOR COMMON FIXED POINT OF STRONGLY NONEXPANSIVE SEQUENCES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 42(3), 719-730. SID. https://sid.ir/paper/703423/en

    Vancouver: Copy

    ZHU WENLONG, LING SHUAI. ITERATIVE SCHEME BASED ON BOUNDARY POINT METHOD FOR COMMON FIXED POINT OF STRONGLY NONEXPANSIVE SEQUENCES. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2016;42(3):719-730. Available from: https://sid.ir/paper/703423/en

    IEEE: Copy

    WENLONG ZHU, and SHUAI LING, “ITERATIVE SCHEME BASED ON BOUNDARY POINT METHOD FOR COMMON FIXED POINT OF STRONGLY NONEXPANSIVE SEQUENCES,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 42, no. 3, pp. 719–730, 2016, [Online]. Available: https://sid.ir/paper/703423/en

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