Strong Convergence Theorem for Two Asymptotically Quasi-Nonexpansive Mappings with Errors in Banach Space

G. S. Saluja

《Tamkang Journal of Mathematics》 38卷1期 (2007/03) Pp. 85-92

並列摘要

In this paper, we study strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if K is a nonempty closed convex subset of a real Banach space E and let S, T: K→K be two asymptotically quasi-nonexpansive mappings with sequences {u(subscript n)}, {v(subscript n)}⊂[0,∞) such that Σ(superscript ∞)(subscript n=1) u(subscript n)＜∞ and Σ(superscript ∞)(subscript n=1) v(subscript n)＜∞, and F=F(S)∩F(T)={x∈K: Sx=Tx=x}≠φ. Suppose {x(subscript n)}(superscript ∞)(subscript n=1) is generated iteratively by x1∈K, and x(subscript n+1)(1-α(subscript n))x(subscript n)+α(subscript n)S(superscript n)y(subscript n)+l(subscript n) y(subscript n)=(1-β(subscript n))x(subscript n)+β(subscript n)T(superscript n)x(subscript n)+m(subscript n), ∀(subscript n)∈N where {l(subscript n)}(superscript ∞)(subscript n=1), {m(subscript n)}(superscript ∞)(subscript n=1) are sequences in K satisfying Σ(superscript ∞)(subscript n=1) ||l(subscript n)||＜∞, Σ(superscript ∞)(subscript n=1) ||m(subscript n)||＜∞, {α(subscript n)}, {β(subscript n)} are real sequences in [0, 1]. It is proved that {x(subscript n)}(superscript ∞)(subscript n=1) converges strongly to some common fixed point of S and T. Our result is significant generalization of corresponding result of Ghosh and Debnath [3], Petryshyn and Williamson [7] and Qihou [8].

並列關鍵字

Asymptotically quasi-nonexpansive mapping ； common fixed point ； the modified Ishikawa iterative sequence with errors ； Banach space