MODIFIED HALPERN ITERATION OF ASYMPTOTICALLY NON-EXPANSIVE MAPPINGS

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SONG Y.; TIAN CH.

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Paper Information

Journal: Bulletin of the Iranian Mathematical Society Year:2009 | Volume:35 | Issue:2 Page(s): 229-254

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Information Journal Paper

Title

MODIFIED HALPERN ITERATION OF ASYMPTOTICALLY NON-EXPANSIVE MAPPINGS

Author(s)

SONG Y. | TIAN CH. | Issue Writer Certificate

Keywords

ASYMPTOTICALLY NON-EXPANSIVE MAPPING

MODIFIED HALPERN ITERATION

UNIFORMLY GATEAUX DIFFERENTIABLE NORM

WEAKLY CONTINUOUS DUALITY

Abstract

For an asymptotically non-expansive self-mapping T, we will prove the strong convergence of {xn} defined by xn+1 = (1−an−bn)xn+anu+bnTnxn, xn+1 = anu+(1−an)Tnxn, whenever {bn}, {an}Ì (0,1) satisfy (C1) limn®¥ an=0, (C2) S¥n=0 =¥ (C3) limn®¥ Kn-1/an = 0 or (C4) S¥n=0 (kn-1)<+¥ application, we also establish the strong convergence of the viscosity approximation schemes with a contraction ¦ given by
xn+1 = anf (xn) + (1 −an)Tnxn
and
xn+1 = (1 −an− bn)xn+an f(xn) +bnTnxn.

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APA: Copy

SONG, Y., & TIAN, CH.. (2009). MODIFIED HALPERN ITERATION OF ASYMPTOTICALLY NON-EXPANSIVE MAPPINGS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 35(2), 229-254. SID. https://sid.ir/paper/560296/en

Vancouver: Copy

SONG Y., TIAN CH.. MODIFIED HALPERN ITERATION OF ASYMPTOTICALLY NON-EXPANSIVE MAPPINGS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2009;35(2):229-254. Available from: https://sid.ir/paper/560296/en

IEEE: Copy

Y. SONG, and CH. TIAN, “MODIFIED HALPERN ITERATION OF ASYMPTOTICALLY NON-EXPANSIVE MAPPINGS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 35, no. 2, pp. 229–254, 2009, [Online]. Available: https://sid.ir/paper/560296/en

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