A perturbed algorithm for a system of variational inclusions involving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mo>⋅</mml:mo><mml:mo>,</mml:mo><mml:mo>⋅</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math>-accretive operators in Banach spaces

Tang, Guo-ji; Wang, Xing

doi:10.1016/j.cam.2014.04.023

Cited by 4 publications

(38 citation statements)

References 14 publications

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“…Remark 4.4. Using the technique in this paper one can extend the results of various authors, see for example [3,6,[7][8][9]18,19,21,[25][26][27][30][31][32][33][34] and the related references cited therein in this direction.…”

Section: Theorem 42mentioning

confidence: 66%

“…which is an important generalization of the problems considered by Chang et al [4], Sahu et al [23] and Tang and Wang [25].…”

Section: Formulation Of the Problem And Existence Of Solutionmentioning

confidence: 95%

“…Among these methods, the resolvent operator techniques for solving variational inclusions have been widely used by many authors. For further study in this direction, we refer to [3,5,6,8,[12][13][14][15][16]18,21,23,25,28,33,34] and the related references therein. In 2014, Sahu et al [23] proved the existence of solutions for a class of nonlinear implicit variational inclusion problems in semi-inner product spaces, which is more general than the results studied in [24].…”

Section: Introductionmentioning

confidence: 99%

“…Using proximal-point operator technique, they studied the convergence analysis of the iterative algorithms for some classes of variational inclusions. For further study of these types of operators and their applications in variational inequalities and variational inclusions, see for example [3,[6][7][8][9][14][15][16]18,19,21,[25][26][27][30][31][32][33][34]. Motivated and inspired by the research work mentioned above, in this paper, we define the generalized resolvent operator associated with (H, ϕ)-η-monotone operator in semi-inner product spaces.…”

Section: Introductionmentioning

confidence: 99%

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Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

Iqbal

Zahoor

2017

Filomat

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In this paper, we consider the system of generalized variational-like inclusion problems in semi-inner product spaces. We define a class of (H, ϕ)-η-monotone operators and its associated class of generalized resolvent operators. Further, using generalized resolvent operator technique, we give the existence of solution of the generalized variational-like inclusion problems. Furthermore, we suggest an iterative algorithm and give the convergence analysis of the sequences generated by the iterative algorithm. The results presented in this paper extend and unify the related known results in the literature.

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Section: Theorem 42mentioning

confidence: 66%

“…which is an important generalization of the problems considered by Chang et al [4], Sahu et al [23] and Tang and Wang [25].…”

Section: Formulation Of the Problem And Existence Of Solutionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

Iqbal

Zahoor

2017

Filomat

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“…From then, the study of the zero points of H -monotone operators in Hilbert space and H -accretive operators in Banach space have received much attention, see Peng (2008), Zou and Huang (2008, 2009), Ahmad and Usman (2009), Wang and Ding (2010), Li and Huang (2011), Tang and Wang (2014) and Huang and Noor (2007), Xia and Huang (2007), Peng and Zhu (2007). Especially, Very recently, Liu and He (2013, 2012) studied the strong and weak convergence for the zero points of H -monotone operators in Hilbert space and H -accretive operators in Banach space respectively.…”

Section: Introductionmentioning

confidence: 99%

Strong convergence theorems for a common zero of a finite family of H-accretive operators in Banach space

Liu

Chen

2016

SpringerPlus

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Graph convergence with an application for system of variational inclusions and fixed-point problems

Balooee

Yao

2022

J Inequal Appl

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This paper aims at proposing an iterative algorithm for finding an element in the intersection of the solutions set of a system of variational inclusions and the fixed-points set of a total uniformly L-Lipschitzian mapping. Applying the concepts of graph convergence and the resolvent operator associated with an Ĥ-accretive mapping, a new equivalence relationship between graph convergence and resolvent-operator convergence of a sequence of Ĥ-accretive mappings is established. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a common point of the above two sets is proved under some suitable hypotheses imposed on the parameters and mappings. At the same time, the notion of $H(\cdot,\cdot)$ H ( ⋅ , ⋅ ) -accretive mapping that appeared in the literature, where $H(\cdot,\cdot)$ H ( ⋅ , ⋅ ) is an α, β-generalized accretive mapping, is also investigated and analyzed. We show that the notions $H(\cdot,\cdot)$ H ( ⋅ , ⋅ ) -accretive and Ĥ-accretive operators are actually the same, and point out some comments on the results concerning them that are available in the literature.

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A perturbed algorithm for a system of variational inclusions involving H(⋅,⋅)-accretive operators in Banach spaces

Cited by 4 publications

References 14 publications

Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

Strong convergence theorems for a common zero of a finite family of H-accretive operators in Banach space

Graph convergence with an application for system of variational inclusions and fixed-point problems

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