Regularization iterative algorithms for monotone and strictly pseudocontractive mappings
نویسندگان
چکیده
منابع مشابه
General iterative methods for monotone mappings and pseudocontractive mappings related to optimization problems
In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a continuous monotone mapping and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Under some control conditions, we establish the strong convergence of the propo...
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Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...
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and Applied Analysis 3 We know that T is pseudocontractive if and only if T satisfies the condition Tx − Ty 2 ≤ x − y 2 + (I − T)x − (I − T)y 2 (15) for all x, y ∈ C. Since u ∈ Fix(T), we have from (15) that ‖Tx − u‖ 2 ≤ ‖x − u‖ 2 + ‖x − Tx‖ 2 , (16) for all x ∈ C. By using (13) and (16), we obtain Tyn − u 2 ≤ yn − u 2 + yn − Tyn 2 = (1 − γn)xn + γnT...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Sciences and Applications
سال: 2016
ISSN: 2008-1901
DOI: 10.22436/jnsa.009.06.38