Viscosity iteration method for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings

Inchan, Issara

doi:10.1016/j.amc.2012.09.020

Cited by 8 publications

References 7 publications

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“…Iterative schemes are of interest in numerical computations and its properties related to acceleration of convergence to solve scientific and engineering problems. A very common iterative scheme is the socalled Jungck iterative scheme, which involves the use of two coupled mappings, and its various extensions, [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such an scheme is useful also in fixed point theory to find common fixed points of both mappings.…”

Section: Introductionmentioning

confidence: 99%

Aitken delta-squared generalized Juncgk-type iterative procedure

Sen¹,

Nistal²

2014

J. Phys.: Conf. Ser.

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Section: Introductionmentioning

confidence: 99%

Aitken delta-squared generalized Juncgk-type iterative procedure

Sen¹,

Nistal²

2014

J. Phys.: Conf. Ser.

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“…Note that, if = 0, scheme (11) reduces to general iterative method (6), which is mainly due to Marino and Xu [10]. If = 0, = 1, and = , scheme (11) reduces to viscosity approximate method introduced by Moudafi [17] and developed by Inchan [18], which also extends the Halpern type results of [19,20] with an idea of mean convergence for -strictly pseudononspreading mapping.…”

Section: Introductionmentioning

confidence: 99%

Strong Convergence of a Unified General Iteration fork-Strictly Pseudononspreading Mapping in Hilbert Spaces

Wen

Chen²,

Tang³

2014

Abstract and Applied Analysis

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We introduce a unified general iterative method to approximate a fixed point ofk-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of ak-strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.

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“…Fixed point theory has an increasing interest in research in the last years especially because of its high richness in bringing together several fields of Mathematics including classical and functional analysis, topology, and geometry [1][2][3][4][5][6][7][8]. There are many fields for the potential application of this rich theory in Physics, Chemistry, and Engineering, for instance, because of its usefulness for the study of existence, uniqueness, and stability of the equilibrium points and for the study of the convergence of state-solution trajectories of differential/difference equations and continuous, discrete, hybrid, and fuzzy dynamic systems as well as the study of the convergence of iterates associated to the solutions.…”

Section: Introductionmentioning

confidence: 99%

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

Sen

Karapınar²

2013

Abstract and Applied Analysis

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This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

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Viscosity iteration method for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings

Cited by 8 publications

References 7 publications

Aitken delta-squared generalized Juncgk-type iterative procedure

Aitken delta-squared generalized Juncgk-type iterative procedure

Strong Convergence of a Unified General Iteration fork-Strictly Pseudononspreading Mapping in Hilbert Spaces

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

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