Taiwanese Journal of Mathematics

HYBRID VISCOSITY ITERATIVE APPROXIMATION OF ZEROS OF M-ACCRETIVE OPERATORS IN BANACH SPACES

L. C. Ceng, A. Petruşel, and M. M. Wong

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Abstract

In this paper, let $X$ be a reflexive Banach space which either is uniformly smooth or has a weakly continuous duality map. We prove, under the convergence of no parameter sequences to zero, the strong convergence of their iterative scheme to a zero of $m$-accretive operator $A$ in $X$, which solves a variational inequality on the set $A^{-1}(0)$ of zeros of $A$. Such a result includes their main result as a special case. Furthermore, we also give a weak convergence theorem for hybrid viscosity iterative approximation method involving a maximal monotone operator in a Hilbert space.

Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2459-2481.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406481

Digital Object Identifier
doi:10.11650/twjm/1500406481

Mathematical Reviews number (MathSciNet)
MR2896128

Zentralblatt MATH identifier
06074771

Subjects
Primary: 47H17 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H05: Monotone operators and generalizations

Keywords
hybrid viscosity iterative approximation method nonexpansive mapping $m$-accretive operator uniformly smooth Banach space reflexive Banach space with weakly continuous duality map

Citation

Ceng, L. C.; Petruşel, A.; Wong, M. M. HYBRID VISCOSITY ITERATIVE APPROXIMATION OF ZEROS OF M-ACCRETIVE OPERATORS IN BANACH SPACES. Taiwanese J. Math. 15 (2011), no. 6, 2459--2481. doi:10.11650/twjm/1500406481. https://projecteuclid.org/euclid.twjm/1500406481


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