Journal of mathematical analysis and applications, ISSN 0022-247X, 2004, Volume 298, Issue 1, pp. 279 - 291

Viscosity approximation methods for nonexpansive mappings are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a Banach space X...

Viscosity approximation | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | BANACH-SPACES | nonexpansive mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Viscosity approximation | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | BANACH-SPACES | nonexpansive mapping | CONVERGENCE | viscosity approximation | FIXED-POINTS

Journal Article

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POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2016, Volume 311, pp. 151 - 179

.... In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier...

Parametrized Navier–Stokes Equation | Proper orthogonal decomposition | Reduced order modelling | RANS | Galerkin projection | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EDDY-VISCOSITY | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | MODELS | CLOSED-LOOP CONTROL | DYNAMICS | Parametrized Navier-Stokes Equation | TURBULENCE | FLOWS | COHERENT STRUCTURES | Numerical analysis | Fluid dynamics | Analysis | Methods | Force and energy

Parametrized Navier–Stokes Equation | Proper orthogonal decomposition | Reduced order modelling | RANS | Galerkin projection | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EDDY-VISCOSITY | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | MODELS | CLOSED-LOOP CONTROL | DYNAMICS | Parametrized Navier-Stokes Equation | TURBULENCE | FLOWS | COHERENT STRUCTURES | Numerical analysis | Fluid dynamics | Analysis | Methods | Force and energy

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2018, Volume 86, Issue 8, pp. 541 - 563

.... The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods...

level set method | incompressible flows | finite elements | multiphase flows | magnetohydrodynamics | pseudo‐spectral methods | pseudo-spectral methods | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | LIQUID | EQUATIONS | MODEL | VARIABLE-DENSITY | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PROJECTION METHOD | REDUCTION CELLS | SIMULATIONS | Fluid dynamics | Viscosity | Industrial production | Compression | Methodology | Aluminum | Fluid flow | Maxwell's equations | Entropy | Spectral methods | Fluids | Solutions | Mathematical models | Mass matrix | Approximation | Computer simulation | Computational fluid dynamics | Momentum | Aluminium | Equations | Incompressible flow | Numerical analysis | Dependent variables | Multiphase | Conducting fluids | Surface tension | Navier-Stokes equations

level set method | incompressible flows | finite elements | multiphase flows | magnetohydrodynamics | pseudo‐spectral methods | pseudo-spectral methods | INSTABILITY | PHYSICS, FLUIDS & PLASMAS | LIQUID | EQUATIONS | MODEL | VARIABLE-DENSITY | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PROJECTION METHOD | REDUCTION CELLS | SIMULATIONS | Fluid dynamics | Viscosity | Industrial production | Compression | Methodology | Aluminum | Fluid flow | Maxwell's equations | Entropy | Spectral methods | Fluids | Solutions | Mathematical models | Mass matrix | Approximation | Computer simulation | Computational fluid dynamics | Momentum | Aluminium | Equations | Incompressible flow | Numerical analysis | Dependent variables | Multiphase | Conducting fluids | Surface tension | Navier-Stokes equations

Journal Article

Mathematical methods in the applied sciences, ISSN 1099-1476, 2018, Volume 42, Issue 1, pp. 250 - 271

.... The method is based on the convergence study of a sequence towards the solution, for which the rates are also given...

global existence result | low‐Mach model | convergence rates | low-Mach model | EXISTENCE | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | NUMBER LIMIT | COMPRESSIBLE FLOWS | SYSTEMS | INCOMPRESSIBLE LIMIT | WELL-POSEDNESS | Viscosity | Iterative methods | Temperature dependence | Numerical Analysis | Analysis of PDEs | Mathematics

global existence result | low‐Mach model | convergence rates | low-Mach model | EXISTENCE | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | NUMBER LIMIT | COMPRESSIBLE FLOWS | SYSTEMS | INCOMPRESSIBLE LIMIT | WELL-POSEDNESS | Viscosity | Iterative methods | Temperature dependence | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 12

In this paper, we study viscosity approximations with ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings...

Halpern type convergence | Mathematical and Computational Biology | ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings | Moudafi’s viscosity approximations | Mathematics | Topology | 54H25 | 47H10 | Browder type convergence | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | (ψ, φ) -weakly contractive mappings | Viscosity | Theorems | Approximation | Texts | Mapping | Approximation methods | Formulas (mathematics) | Convergence

Halpern type convergence | Mathematical and Computational Biology | ( ψ , φ ) $(\psi,\varphi)$ -weakly contractive mappings | Moudafi’s viscosity approximations | Mathematics | Topology | 54H25 | 47H10 | Browder type convergence | Analysis | Mathematics, general | Applications of Mathematics | Differential Geometry | (ψ, φ) -weakly contractive mappings | Viscosity | Theorems | Approximation | Texts | Mapping | Approximation methods | Formulas (mathematics) | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

We combine a sequence of contractive mappings and propose a generalized viscosity approximation method...

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | contractive mapping | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | Contractive mapping | Variational inequality | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | FAMILIES | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Fixed point theory | Usage | Approximation theory | Distributions, Theory of (Functional analysis) | Contraction operators | Viscosity | Approximation | Mathematical analysis | Inequalities | Hilbert space | Mapping | Iterative methods | Convergence

Mathematical and Computational Biology | fixed point | Analysis | viscosity approximation method | contractive mapping | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | Contractive mapping | Variational inequality | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | FAMILIES | STRONG-CONVERGENCE THEOREMS | FIXED-POINTS | Fixed point theory | Usage | Approximation theory | Distributions, Theory of (Functional analysis) | Contraction operators | Viscosity | Approximation | Mathematical analysis | Inequalities | Hilbert space | Mapping | Iterative methods | Convergence

Journal Article

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Viscosity approximation methods for asymptotically nonexpansive mapping in CAT(0) spaces

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 15

...Wangkeeree et al. Fixed Point Theory and Applications null2015)null015:23null DOI 10.1186/s13663-015-0273-x R E S E A R C H Open Access Viscosity approximation...

Mathematical and Computational Biology | Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | asymptotically nonexpansive mapping | MATHEMATICS | SEMIGROUPS | CONVERGENCE THEOREMS | FIXED-POINTS | Viscosity | Fixed point theory | Approximation theory | Methods | Theorems | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Mapping | Convergence

Mathematical and Computational Biology | Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | Mathematics | variational inequality | Applications of Mathematics | Topology | Differential Geometry | asymptotically nonexpansive mapping | MATHEMATICS | SEMIGROUPS | CONVERGENCE THEOREMS | FIXED-POINTS | Viscosity | Fixed point theory | Approximation theory | Methods | Theorems | Approximation | Asymptotic properties | Mathematical analysis | Inequalities | Mapping | Convergence

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2016, Volume 13, Issue 5, pp. 2645 - 2657

Based on some iteration schemes, we study the viscosity approximation results for multivalued nonexpansive mappings in Hilbert space and Banach space...

Secondary 49J40 | Multivalued nonexpansive mapping | 47H09 | Mathematics, general | Mathematics | variational inequality | fixed-point theorems | Primary 47H10 | MATHEMATICS | MATHEMATICS, APPLIED | ISHIKAWA ITERATION | MANN | CONVERGENCE | FIXED-POINTS

Secondary 49J40 | Multivalued nonexpansive mapping | 47H09 | Mathematics, general | Mathematics | variational inequality | fixed-point theorems | Primary 47H10 | MATHEMATICS | MATHEMATICS, APPLIED | ISHIKAWA ITERATION | MANN | CONVERGENCE | FIXED-POINTS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 15

The purpose of this paper is to study the strong convergence theorems of Moudafi’s viscosity approximation methods for a nonexpansive mapping T in CAT(0...

Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Common fixed point | Variational inequality | Viscosity approximation method | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE THEOREMS

Analysis | viscosity approximation method | CAT space | common fixed point | Mathematics, general | nonexpansive mapping | Mathematics | variational inequality | Applications of Mathematics | Common fixed point | Variational inequality | Viscosity approximation method | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE THEOREMS

Journal Article

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Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces

Journal of mathematical analysis and applications, ISSN 0022-247X, 2007, Volume 325, Issue 1, pp. 469 - 479

The aim of this work is to propose implicit and explicit viscosity-like methods for finding specific common fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces...

Nearest point projection | Common fixed point | Convex optimization | Viscosity method | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | viscosity method | nearest point projection | FINITE FAMILY | common fixed point | nonexpansive mapping | convex optimization | CONVERGENCE | IMPLICIT ITERATION PROCESS | Analysis | Methods | Algorithms

Nearest point projection | Common fixed point | Convex optimization | Viscosity method | Nonexpansive mapping | MATHEMATICS | MATHEMATICS, APPLIED | viscosity method | nearest point projection | FINITE FAMILY | common fixed point | nonexpansive mapping | convex optimization | CONVERGENCE | IMPLICIT ITERATION PROCESS | Analysis | Methods | Algorithms

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2016, Volume 19, Issue 2, pp. 1481 - 1499

In this paper, we introduce the strong convergence theorem for the viscosity approximation methods for solving the split common fixed-point problem in Hilbert spaces...

Split null point problem | Fixed-point theory | Split feasibility problem | Split common fixed-point problem | Split variational inequality problem | MATHEMATICS | MATHEMATICS, APPLIED | SET | ALGORITHMS

Split null point problem | Fixed-point theory | Split feasibility problem | Split common fixed-point problem | Split variational inequality problem | MATHEMATICS | MATHEMATICS, APPLIED | SET | ALGORITHMS

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 10/2018, Volume 39, Issue 13, pp. 1374 - 1406

In this article, we study viscosity approximation methods for generalized multi-valued nonexpansive mappings and we present some new results related to strong convergence, variational inequality...

split feasibility problem | variational inequality | Condition (C) | viscosity approximation | Primary 47H10 | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | STRONG-CONVERGENCE THEOREMS | OPERATORS | Viscosity | Computational geometry | Approximation | Convexity | Mathematical analysis | Optimization

split feasibility problem | variational inequality | Condition (C) | viscosity approximation | Primary 47H10 | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | STRONG-CONVERGENCE THEOREMS | OPERATORS | Viscosity | Computational geometry | Approximation | Convexity | Mathematical analysis | Optimization

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 13

In this paper, we introduce several types of viscosity approximation methods for nonexpansive nonself-mappings in certain Banach spaces...

boundary condition | sunny nonexpansive retraction | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | nonexpansive nonself-mapping | Applications of Mathematics | Topology | Differential Geometry | viscosity approximation | Nonexpansive nonself-mapping | Boundary condition | Viscosity approximation | Fixed point | Sunny nonexpansive retraction | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | BANACH-SPACES | STRONG-CONVERGENCE THEOREMS | Viscosity | Fixed point theory | Usage | Approximation theory | Contraction operators | Theorems | Approximation | Mathematical analysis | Boundary conditions | Banach space | Convergence

boundary condition | sunny nonexpansive retraction | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | Mathematics | nonexpansive nonself-mapping | Applications of Mathematics | Topology | Differential Geometry | viscosity approximation | Nonexpansive nonself-mapping | Boundary condition | Viscosity approximation | Fixed point | Sunny nonexpansive retraction | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | BANACH-SPACES | STRONG-CONVERGENCE THEOREMS | Viscosity | Fixed point theory | Usage | Approximation theory | Contraction operators | Theorems | Approximation | Mathematical analysis | Boundary conditions | Banach space | Convergence

Journal Article

SIAM journal on scientific computing, ISSN 1095-7197, 2010, Volume 32, Issue 3, pp. 1159 - 1179

Modeling and numerical approximation of two-phase incompressible flows with different densities and viscosities are considered...

Navier-Stokes | Phase-field | Stability | Variable density | Two-phase flow | Projection methods | FLUIDS | MATHEMATICS, APPLIED | projection methods | NAVIER-STOKES EQUATIONS | 2ND-ORDER | VARIABLE-DENSITY | variable density | stability | phase-field | two-phase flow | Studies | Viscosity | Mathematical models | Numerical analysis | Fluid dynamics | Density

Navier-Stokes | Phase-field | Stability | Variable density | Two-phase flow | Projection methods | FLUIDS | MATHEMATICS, APPLIED | projection methods | NAVIER-STOKES EQUATIONS | 2ND-ORDER | VARIABLE-DENSITY | variable density | stability | phase-field | two-phase flow | Studies | Viscosity | Mathematical models | Numerical analysis | Fluid dynamics | Density

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 5/2011, Volume 49, Issue 1, pp. 179 - 192

.... We propose a class of vector-valued generalized viscosity approximation method for solving the problem...

Weak Pareto optimal solution | Asymptotic function | Generalized viscosity method | Convex and Discrete Geometry | Operations Research/Decision Theory | Multiobjective optimization | Asymptotic cone | Mathematics | Statistics, general | Operations Research, Mathematical Programming | Optimization | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | VARIATIONAL INEQUALITY PROBLEMS | PROXIMAL METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | Universities and colleges | Mathematical optimization | Pareto efficiency | Methods | Viscosity | Studies | Pareto optimum | Asymptotic methods | Approximations

Weak Pareto optimal solution | Asymptotic function | Generalized viscosity method | Convex and Discrete Geometry | Operations Research/Decision Theory | Multiobjective optimization | Asymptotic cone | Mathematics | Statistics, general | Operations Research, Mathematical Programming | Optimization | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | VARIATIONAL INEQUALITY PROBLEMS | PROXIMAL METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | EQUILIBRIUM PROBLEMS | FIXED-POINT PROBLEMS | Universities and colleges | Mathematical optimization | Pareto efficiency | Methods | Viscosity | Studies | Pareto optimum | Asymptotic methods | Approximations

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 7/2018, Volume 41, Issue 3, pp. 1561 - 1579

...Bull. Malays. Math. Sci. Soc. (2018) 41:1561–1579 https://doi.org/10.1007/s40840-016-0413-4 Viscosity Approximation Methods for Implicit Midpoint Rule...

34G20 | Implicit midpoint rule | Mathematics, general | Mathematics | Applications of Mathematics | 47J25 | 47N10 | Viscosity approximation method | CAT space | 65J15 | Nonexpansive mapping | HARMONIC MAPS | CAT METRIC-SPACES | MATHEMATICS | BANACH-SPACES | THEOREMS | CURVATURE | CAT space | CONVERGENCE | ORDINARY DIFFERENTIAL-EQUATIONS | FIXED-POINTS | Viscosity | Approximation | Convergence

34G20 | Implicit midpoint rule | Mathematics, general | Mathematics | Applications of Mathematics | 47J25 | 47N10 | Viscosity approximation method | CAT space | 65J15 | Nonexpansive mapping | HARMONIC MAPS | CAT METRIC-SPACES | MATHEMATICS | BANACH-SPACES | THEOREMS | CURVATURE | CAT space | CONVERGENCE | ORDINARY DIFFERENTIAL-EQUATIONS | FIXED-POINTS | Viscosity | Approximation | Convergence

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2010, Volume 59, Issue 1, pp. 74 - 79

In this paper, we discuss the strong convergence of the viscosity approximation method, in Hilbert spaces, relatively to the computation of fixed points of operators in the wide class of quasi-nonexpansive mappings...

Convex minimization | Bilevel optimization | Quasi-nonexpansive operator | Variational inequality | Viscosity approximation method | Fixed point method | WEAK | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | THEOREMS | FIXED-POINTS | STRONG-CONVERGENCE | Mathematics | Optimization and Control

Convex minimization | Bilevel optimization | Quasi-nonexpansive operator | Variational inequality | Viscosity approximation method | Fixed point method | WEAK | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | THEOREMS | FIXED-POINTS | STRONG-CONVERGENCE | Mathematics | Optimization and Control

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2007, Volume 331, Issue 1, pp. 506 - 515

In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points...

Equilibrium problem | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | fixed point | viscosity approximation method | equilibrium problem | nonexpansive mapping

Equilibrium problem | Viscosity approximation method | Nonexpansive mapping | Fixed point | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | fixed point | viscosity approximation method | equilibrium problem | nonexpansive mapping

Journal Article