On a new system of generalized mixed quasi-variational-like inclusions with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>,</mml:mo><mml:mi>η</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-accretive operators in real<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-uniformly smooth Banach spaces

Peng, Jian-Wen

doi:10.1016/j.na.2006.11.054

Cited by 18 publications

(18 citation statements)

References 33 publications

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“…For these reasons, many existence result and iterative algorithms for various variational inclusion have been studied. For details, we refer the reader to [1][2][3][4][5][6][7][8][9][10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

Feng

Ding

2009

Journal of Computational and Applied Mathematics

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Iterative algorithm System of generalized nonlinear quasi-variational-like inclusions a b s t r a c tIn this paper, we study some properties of A-monotone operator in Banach space, give the notion of proximal mapping associated with the A-monotone operator and show its Lipschitz continuity. We also consider a new system of generalized nonlinear quasivariational-like inclusions with A-monotone operators in Banach spaces and constructed a new iterative algorithm for solving the system of generalized nonlinear quasi-variationallike inclusions in Banach spaces. Under suitable assumptions, we prove the convergence of the iterative sequences generated by the algorithm.

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Section: Introductionmentioning

confidence: 99%

A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

Feng

Ding

2009

Journal of Computational and Applied Mathematics

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“…By (10), we know that 0 < χ < 1 and hence there exist n 0 > 0 and χ 0 ∈ (0, 1) such that χ n+1 ≤ χ 0 for all n ≥ n 0 . Therefore, by (23) we have …”

Section: Xie-ping Ding and Zhong-bao Wangmentioning

confidence: 97%

“…We emphasize that H-η-monotone operators in Banach spaces are completely different from (A, η)-accretive operators introduced in Refs. [12][13]23]. Definition 1.3 [10] Let η : E × E → E and H : E → E * be two single-valued mappings, and M :…”

Section: Remark 11mentioning

confidence: 99%

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

Ding

Wang

2009

Appl. Math. Mech.-Engl. Ed.

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A new system of the set-valued mixed quasi-variational-like inclusions (SS-MQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

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“…Consequently, it is clear that the variational-like inequality problems are only well defined in the setting of invexity. We would like to point out that the basic concepts defined in [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] have many technical flaws. Consequently all the results obtained in these and related papers do not make any sense and are misleading.…”

Section: Introductionmentioning

confidence: 99%

Vector nonsmooth variational-like inequalities and optimization problems

Farajzadeh

Noor

2009

Nonlinear Analysis: Theory, Methods & Applications

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On a new system of generalized mixed quasi-variational-like inclusions with(H,η)-accretive operators in realq-uniformly smooth Banach spaces

Cited by 18 publications

References 33 publications

A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

Vector nonsmooth variational-like inequalities and optimization problems

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