Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces

Ahmad, Rais; Siddiqi, Abul Hasan; Khan, Zaheer

doi:10.1016/j.amc.2004.02.021

Cited by 19 publications

(22 citation statements)

References 16 publications

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“…By using the h proximal mapping technique, we prove the existence of solutions and approximate the solutions by some new N -step iterative algorithms. Our results extend and improve some known results in the references [1][2][3][4][5][6][7][8][9].…”

Section: Introductionsupporting

confidence: 76%

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A new system of generalized quasi-variational-like inclusions with noncompact valued mappings

Cao

2012

J Inequal Appl

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In this article, we introduce and study a new system of generalized quasi-variationallike inclusions with noncompact valued mappings. By using the h-proximal mapping technique, we prove the existence of solutions and the convergence of some new N-step iterative algorithms for this system of generalized quasi-variational-like inclusions. Our results extend and improve some known results in the literature.

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Section: Introductionsupporting

confidence: 76%

“…For more special cases, please refer to [1][2][3][4][5][6][7][8][9] and the references therein. Remark 1.1.…”

Section: Introductionmentioning

confidence: 99%

A new system of generalized quasi-variational-like inclusions with noncompact valued mappings

Cao

2012

J Inequal Appl

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“…(see, for example, [1][2][3][4][5][6][7]). The resolvent operator techniques for solving variational inequalities and variational inclusions are interesting and important.…”

Section: Introductionmentioning

confidence: 99%

Mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces

Ahmad

Siddiqi

2007

Journal of Mathematical Analysis and Applications

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In this paper, we study mixed variational-like inclusions and J η -proximal operator equations in Banach spaces. It is established that mixed variational-like inclusions in real Banach spaces are equivalent to fixed point problems. We also establish a relationship between mixed variational-like inclusions and J η -proximal operator equations. This equivalence is used to suggest an iterative algorithm for solving J η -proximal operator equations.

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“…. N ·, · , then problem 2.14 reduces to a problem considered by Chang, et al 12, 13 that is, find u ∈ H, w 1 …”

Section: Special Casesmentioning

confidence: 99%

Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings

Ahmad¹,

Dilshad²

2011

Fixed Point Theory and Applications

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Proximal point algorithm for generalized multivalued nonlinear quasi-variational-like inclusions in Banach spaces

Cited by 19 publications

References 16 publications

A new system of generalized quasi-variational-like inclusions with noncompact valued mappings

A new system of generalized quasi-variational-like inclusions with noncompact valued mappings

Mixed variational-like inclusions and Jη-proximal operator equations in Banach spaces

Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings

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