Local convergence radius for the Mann-type iteration [PDF]
Annals of the West University of Timisoara: Mathematics and Computer Science, 2015 A procedure to estimate the local convergence radius for a Mann-type iteration is given in the setting of a finite dimensional space. In particular we obtain the estimation of radius for classical Newton method.
Măruşter Ştefan
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Implicit Mann Type Iteration Method Involving Strictly Hemicontractive Mappings in Banach Spaces [PDF]
Journal of Applied Mathematics, 2012 We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach spaces.
Arif Rafiq, Shin Min Kang
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Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems [PDF]
Mathematics, 2019 This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of ...
Lu-Chuan Ceng, Xiaoye Yang
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Some Modified Mann-Type Inertial Forward–Backward Iterative Methods for Monotone Inclusion Problems
MathematicsIn this paper, we propose three variants of Mann-type inertial forward–backward iterative methods for approximating the minimum-norm solution of the monotone inclusion problem and the fixed points of nonexpansive mappings.
Mohammad Dilshad +3 more
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Rates of ($T$-)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration [PDF]
Portugaliae MathematicaIn this paper, we use proof mining methods to compute rates of ( T -)asymptotic regularity of the generalized Krasnoselskii–Mann-type iteration associated to a nonexpansive mapping T:X\to X
Paulo Firmino, Laurenţiu Leuştean
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On the Mann-type iteration and the convex feasibility problem
Journal of Computational and Applied Mathematics, 2008 Let \(C\) be a closed convex subset of a Hilbert space \(H\); and \(T:C\to C\) be a nonlinear map with nonempty fixed point set \(F(T)\) in \(C\) fulfilling (a) \(T\) is \(p\)-demicontractive on \(C\), (b) \(I-T\) is demiclosed at zero. Let \((x_k)\) be the Mann-type iterative process \[ x_{k+1}=(1-t_k)x_k+t_kT(x_k); \quad k\geq 0, \] where \(x_0\in C\)
Măruşter, Ştefan, Popirlan, Cristina
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Mann-Type Extragradient Methods for General Systems of Variational Inequalities with Multivalued Variational Inclusion Constraints in Banach Spaces [PDF]
Abstract and Applied Analysis, 2013 We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces.
Lu-Chuan Ceng +2 more
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A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems [PDF]
Abstract and Applied Analysis, 2011 A new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in ...
Utith Inprasit, Weerayuth Nilsrakoo
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The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems [PDF]
Abstract and Applied Analysis, 2013 The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split ...
Lu-Chuan Ceng +2 more
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On some Mann’s type iterative algorithms [PDF]
Fixed Point Theory and Applications, 2015 AbstractFirst we present some interesting variants of Mann’s method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients.
Luigi Muglia +4 more
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