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- W1520805519 abstract "Recently, H. K. Xu [J. Math. Anal. Appl. 314 (2006) 631-643] considered the iterative method for approximation to zeros of an $m$-accretive operator $A$ in a Banach space $X$. In this paper, we propose a hybrid viscosity approximation method with perturbed mapping that generates the sequence ${x_n}$ by the algorithm $x_{n+1} = alpha_n(u+f(x_n)) + (1-alpha_n) [J_{r_n} x_n - lambda_n F(J_{r_n} x_n)]$, where ${alpha_n}$, ${r_n}$ and ${lambda_n}$ are three sequences satisfying certain conditions, $f$ is a contraction on $X$, $J_r$ denotes the resolvent $(I+rA)^{-1}$ for $r gt 0$, and $F$ is a perturbed mapping which is both $delta$-strongly accretive and $lambda$-strictly pseudocontractive with $delta + lambda geq 1$. Under the assumption that $X$ either has a weakly continuous duality map or is uniformly smooth, we establish some strong convergence theorems for this hybrid viscosity approximation method with perturbed mapping." @default.
- W1520805519 created "2016-06-24" @default.
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- W1520805519 date "2007-08-01" @default.
- W1520805519 modified "2023-09-23" @default.
- W1520805519 title "STRONG CONVERGENCE OF A HYBRID VISCOSITY APPROXIMATION METHOD WITH PERTURBED MAPPINGS FOR NONEXPANSIVE AND ACCRETIVE OPERATORS" @default.
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- W1520805519 doi "https://doi.org/10.11650/twjm/1500404751" @default.
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