On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems

Marino, Giuseppe; Muglia, Luigi

doi:10.1007/s11590-013-0705-7

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Convergence Of An Iterative Scheme1

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Cited by 6 publications

(2 citation statements)

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“…Note that, if (W n ) n∈N is generated using a suitable procedure (for instance, a uniformly asymptotically regular (UAR) procedure, see [14,15]), hypothesis (H3) reduces to a hypothesis the sequences implemented in the procedure itself.…”

Section: Convergence Of An Iterative Schemementioning

confidence: 99%

On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients

Hussain

Marino

Muglia

et al. 2015

J. Fixed Point Theory Appl.

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Section: Convergence Of An Iterative Schemementioning

confidence: 99%

On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients

Hussain

Marino

Muglia

et al. 2015

J. Fixed Point Theory Appl.

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“…strong convergence of which was proved in [29] in uniformly convex and uniformly smooth Banach spaces under conditions (t), (β), [24], replacing (ii) in the definition of W k by lim k→∞ W k+1 x− W k x = 0 uniformly in x ∈ B and combining the steepest-descent method with the Krasnosel'skii-Mann one, studied the methods…”

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Steepest-descent Ishikawa iterative methods for a class of variational inequalities in Banach spaces

Buong

Quynh²,

Thi

2020

Filomat

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In this paper, for finding a fixed point of a nonexpansive mapping in either uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly G?teaux differentiable norm, we present a new explicit iterative method, based on a combination of the steepest-descent method with the Ishikawa iterative one. We also show its several particular cases one of which is the composite Halpern iterative method in literature. The explicit iterative method is also extended to the case of infinite family of nonexpansive mappings. Numerical experiments are given for illustration.

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On the Approximation of Zeros of Non-Self Monotone Operators

Colao

Marino

Muglia

2016

Numerical Functional Analysis and Optimization

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On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems

Cited by 6 publications

References 34 publications

On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients

On the strong convergence of a general-type Krasnosel’skii–Mann’s algorithm depending on the coefficients

Steepest-descent Ishikawa iterative methods for a class of variational inequalities in Banach spaces

On the Approximation of Zeros of Non-Self Monotone Operators

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