Numerical Algorithms, ISSN 1017-1398, 9/2017, Volume 76, Issue 1, pp. 259 - 282

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of...

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Journal Article

Demonstratio mathematica, ISSN 2391-4661, 2018, Volume 51, Issue 1, pp. 277 - 294

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a...

minimization problem | 47H09 | 47J05 | demimetric mappings | 47J25 | fixed point problem | 47H06 | CAT spaces

minimization problem | 47H09 | 47J05 | demimetric mappings | 47J25 | fixed point problem | 47H06 | CAT spaces

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2018, Volume 2018, Issue 1, pp. 1 - 14

Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E∗ $E^{*}$. In this paper,...

Mathematical and Computational Biology | Relatively nonexpansive maps | Mathematics | Topology | 47H10 | 47J20 | Variational inequality | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Subgradient extragradient algorithm | Differential Geometry | 47J25 | Theorems | Fixed points (mathematics) | Iterative algorithms | Banach space

Mathematical and Computational Biology | Relatively nonexpansive maps | Mathematics | Topology | 47H10 | 47J20 | Variational inequality | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Subgradient extragradient algorithm | Differential Geometry | 47J25 | Theorems | Fixed points (mathematics) | Iterative algorithms | Banach space

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2018, Volume 2018, Issue 1, pp. 1 - 9

In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly...

Strong convergence | Mathematical and Computational Biology | Relatively nonexpansive maps | Mathematics | Topology | Generalised projection | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | Inertial algorithm

Strong convergence | Mathematical and Computational Biology | Relatively nonexpansive maps | Mathematics | Topology | Generalised projection | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | Inertial algorithm

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2018, Volume 2018, Issue 1, pp. 1 - 21

In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong...

Mathematical and Computational Biology | Null point problem | Variational inequality problem | Mathematics | Topology | Fixed point problem | Demicontractive mappings | Equilibrium problem | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Differential Geometry | 47J25 | 47N10 | Decision making models | Hilbert space

Mathematical and Computational Biology | Null point problem | Variational inequality problem | Mathematics | Topology | Fixed point problem | Demicontractive mappings | Equilibrium problem | Analysis | 47H09 | Mathematics, general | 47J05 | Applications of Mathematics | Differential Geometry | 47J25 | 47N10 | Decision making models | Hilbert space

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 10

In this study, we introduce a class of new generalized parametric nonlinear ordered variational inequality problems and discuss its existence result. Also, we...

Restricted-accretive | 47J22 | 47J20 | Sensitivity analysis | Variational inequality | Analysis | Mathematics, general | Parametric | Mathematics | 47J05 | Applications of Mathematics | Ordered Banach spaces | MATHEMATICS | MATHEMATICS, APPLIED | Economic models | Banach spaces | Banach space | Portfolio management | Inequality

Restricted-accretive | 47J22 | 47J20 | Sensitivity analysis | Variational inequality | Analysis | Mathematics, general | Parametric | Mathematics | 47J05 | Applications of Mathematics | Ordered Banach spaces | MATHEMATICS | MATHEMATICS, APPLIED | Economic models | Banach spaces | Banach space | Portfolio management | Inequality

Journal Article

Advances in pure and applied mathematics (Berlin, Germany), ISSN 1869-6090, 2018, Volume 9, Issue 3, pp. 167 - 184

In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is...

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

convex minimization problem | Legendre functions | Gâteaux differentiable function | Bregman distance | strong convergence | Bregman projection | Fréchet differentiable functions | 47H09 | variational inequality, reflexive Banach space | 47J05 | 47J25 | resolvent | 47H06 | reffexive Banach space | variational inequality | Iterative algorithms | Error analysis | Banach spaces | Banach space | Optimization

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2018, Volume 2018, Issue 1, pp. 1 - 14

In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real...

Monotone mappings | Mathematical and Computational Biology | Pseudocontractive mappings | Mathematics | 37C25 | Topology | 47H10 | Analysis | Mathematics, general | Fixed points | 47J05 | Applications of Mathematics | Differential Geometry | Iterative methods | Hilbert space | Approximation

Monotone mappings | Mathematical and Computational Biology | Pseudocontractive mappings | Mathematics | 37C25 | Topology | 47H10 | Analysis | Mathematics, general | Fixed points | 47J05 | Applications of Mathematics | Differential Geometry | Iterative methods | Hilbert space | Approximation

Journal Article

Numerical Algorithms, ISSN 1017-1398, 11/2019, Volume 82, Issue 3, pp. 1047 - 1063

In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings...

Numeric Computing | Theory of Computation | Split common fixed-point problem | 54H25 | Weak convergence | 47H10 | Algorithms | Algebra | Dual variable | Averaged mapping | Numerical Analysis | Computer Science | 47H09 | Iterative algorithm | Hilbert space | 47J05 | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | MANN ALGORITHM | CONVEX FEASIBILITY | PROJECTION | CONVERGENCE | CQ-ALGORITHM

Numeric Computing | Theory of Computation | Split common fixed-point problem | 54H25 | Weak convergence | 47H10 | Algorithms | Algebra | Dual variable | Averaged mapping | Numerical Analysis | Computer Science | 47H09 | Iterative algorithm | Hilbert space | 47J05 | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | MANN ALGORITHM | CONVEX FEASIBILITY | PROJECTION | CONVERGENCE | CQ-ALGORITHM

Journal Article

10.
Full Text
A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1812, 2019, Volume 2019, Issue 1, pp. 1 - 19

Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates...

Strong convergence | Mathematical and Computational Biology | Variational inequality problem | Mathematics | Topology | Generalized- Φ -strongly monotone map | Analysis | 47H09 | Mathematics, general | Hammerstein integral equation | 47J05 | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | Optimization problem | Generalized-Φ-strongly monotone map | Computational geometry | Theorems | Algorithms | Maps | Integral equations | Iterative algorithms | Convexity | Iterative methods | Banach space | Portfolio management | Optimization | Convergence

Strong convergence | Mathematical and Computational Biology | Variational inequality problem | Mathematics | Topology | Generalized- Φ -strongly monotone map | Analysis | 47H09 | Mathematics, general | Hammerstein integral equation | 47J05 | Applications of Mathematics | Differential Geometry | 47H05 | 47J25 | Optimization problem | Generalized-Φ-strongly monotone map | Computational geometry | Theorems | Algorithms | Maps | Integral equations | Iterative algorithms | Convexity | Iterative methods | Banach space | Portfolio management | Optimization | Convergence

Journal Article

11.
Full Text
Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

数学学报：英文版, ISSN 1439-8516, 2016, Volume 32, Issue 11, pp. 1357 - 1376

Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem...

split common fixed point problems | Demicontractive mappings | 47H09 | Mathematics, general | Hilbert spaces | Mathematics | 47J05 | iterative scheme | 47J25 | 47H06 | strong convergence | ITERATION | MATHEMATICS, APPLIED | VARIATIONAL INEQUALITY PROBLEM | CYCLIC ALGORITHM | CQ ALGORITHM | MATHEMATICS | PROJECTION | SETS | MAPPINGS | STRONG-CONVERGENCE | Computer science | Investigations | Algorithms | Studies | Mapping | Hilbert space | Mathematical analysis | Approximations | Operators | Fixed points (mathematics) | Norms | Mathematical models | Convergence

split common fixed point problems | Demicontractive mappings | 47H09 | Mathematics, general | Hilbert spaces | Mathematics | 47J05 | iterative scheme | 47J25 | 47H06 | strong convergence | ITERATION | MATHEMATICS, APPLIED | VARIATIONAL INEQUALITY PROBLEM | CYCLIC ALGORITHM | CQ ALGORITHM | MATHEMATICS | PROJECTION | SETS | MAPPINGS | STRONG-CONVERGENCE | Computer science | Investigations | Algorithms | Studies | Mapping | Hilbert space | Mathematical analysis | Approximations | Operators | Fixed points (mathematics) | Norms | Mathematical models | Convergence

Journal Article

Numerical algorithms, ISSN 1572-9265, 2017, Volume 79, Issue 2, pp. 529 - 553

Using the double projection and Halpern methods, we prove two strong convergence results for finding a solution of a variational inequality problem involving...

Quasi-nonexpansive mapping | Monotone mappings | Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Algorithms | Algebra | Numerical Analysis | Double projection Method | Computer Science | 47H09 | Halpern method | 47J05 | 47J25 | 47H06 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | THEOREM | HYBRID METHOD | STEP | SUBGRADIENT EXTRAGRADIENT METHOD | BANACH-SPACES | GRADIENT-METHOD | STRONG-CONVERGENCE

Quasi-nonexpansive mapping | Monotone mappings | Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Algorithms | Algebra | Numerical Analysis | Double projection Method | Computer Science | 47H09 | Halpern method | 47J05 | 47J25 | 47H06 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | THEOREM | HYBRID METHOD | STEP | SUBGRADIENT EXTRAGRADIENT METHOD | BANACH-SPACES | GRADIENT-METHOD | STRONG-CONVERGENCE

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 180, Issue 1, pp. 140 - 169

For constrained equations with nonisolated solutions, we show that if the equation mapping is 2-regular at a given solution with respect to a direction in the...

Piecewise Newton method | Newton-type method | 65K15 | Nonisolated solution | Mathematics | Theory of Computation | Complementarity problem | LP-Newton method | Optimization | Constrained equation | Levenberg–Marquardt method | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 90C33 | 2-Regularity | 47J05 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | CONVERGENCE PROPERTIES | Levenberg-Marquardt method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR EQUATIONS | SYSTEMS | Mathematical analysis | Newton methods | Convergence

Piecewise Newton method | Newton-type method | 65K15 | Nonisolated solution | Mathematics | Theory of Computation | Complementarity problem | LP-Newton method | Optimization | Constrained equation | Levenberg–Marquardt method | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | 90C33 | 2-Regularity | 47J05 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | CONVERGENCE PROPERTIES | Levenberg-Marquardt method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR EQUATIONS | SYSTEMS | Mathematical analysis | Newton methods | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 16

This manuscript deals with two general systems of nonlinear ordered variational inclusion problems. We also construct some new iterative algorithms for finding...

47J20 | Analysis | Mathematics, general | Nonlinear ordered variational inclusions | Mathematics | 47J05 | Applications of Mathematics | Algorithm | Weak-ARD mapping | System | Ordered Hilbert space | Iterative algorithms | Hilbert space | Inclusions | Nonlinear systems | Research

47J20 | Analysis | Mathematics, general | Nonlinear ordered variational inclusions | Mathematics | 47J05 | Applications of Mathematics | Algorithm | Weak-ARD mapping | System | Ordered Hilbert space | Iterative algorithms | Hilbert space | Inclusions | Nonlinear systems | Research

Journal Article

Numerical Algorithms, ISSN 1017-1398, 6/2016, Volume 72, Issue 2, pp. 467 - 481

In this paper, we propose a new simple explicit iterative algorithm to find a solution for variational inequalities over the set of common fixed points of an...

Algorithms | Algebra | Variational inequality | 49J30 | Numerical Analysis | Computer Science | Numeric Computing | 47H09 | Theory of Computation | 47J05 | Nonexpansive mapping | Fixed point | MATHEMATICS, APPLIED | ALGORITHM | STRONG-CONVERGENCE THEOREMS | STEEPEST-DESCENT | FIXED-POINTS | FAMILY | Methods

Algorithms | Algebra | Variational inequality | 49J30 | Numerical Analysis | Computer Science | Numeric Computing | 47H09 | Theory of Computation | 47J05 | Nonexpansive mapping | Fixed point | MATHEMATICS, APPLIED | ALGORITHM | STRONG-CONVERGENCE THEOREMS | STEEPEST-DESCENT | FIXED-POINTS | FAMILY | Methods

Journal Article

Journal of Applied Analysis, ISSN 1425-6908, 12/2015, Volume 21, Issue 2, pp. 63 - 77

In this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite...

equilibrium problem | 47H09 | reflexive Banach spaces | Legendre function | 47J05 | Bregman distance | 47J25 | resolvent | 47H06 | strong convergence

equilibrium problem | 47H09 | reflexive Banach spaces | Legendre function | 47J05 | Bregman distance | 47J25 | resolvent | 47H06 | strong convergence

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2016, Volume 36, Issue 5, pp. 1474 - 1486

Let H1, H2, H3 be real Hilbert spaces, let A: H1 → H3, B: H2 → H3 be two bounded linear operators. The split equality common fixed point problem (SECFP) in the...

viscosity iterative algorithms | 47H10 | split equality common fixed point problems | 47H09 | Hilbert space | 47J05 | quasi-nonexpansive operator | strong convergence | 54H25 | MATHEMATICS | PROJECTION | CONVEX FEASIBILITY | CQ ALGORITHM

viscosity iterative algorithms | 47H10 | split equality common fixed point problems | 47H09 | Hilbert space | 47J05 | quasi-nonexpansive operator | strong convergence | 54H25 | MATHEMATICS | PROJECTION | CONVEX FEASIBILITY | CQ ALGORITHM

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2018, Volume 26, Issue 2, pp. 327 - 352

We present a new covering theorem for a nonlinear mapping on a convex cone, under the assumptions weaker than the classical Robinson’s regularity condition....

Nonisolated solution | Stability | Probability Theory and Stochastic Processes | Covering | Mathematics | Complementarity problem | Generalized Nash equilibrium problem | Constrained equation | Sensitivity | 49J53 | Analysis | 90C33 | Singular solution | 47J05 | COINCIDENCE POINTS | MATHEMATICS, APPLIED | MULTIFUNCTIONS | MAPS | GENERALIZED EQUATIONS | THEOREMS | CONE | Game theory

Nonisolated solution | Stability | Probability Theory and Stochastic Processes | Covering | Mathematics | Complementarity problem | Generalized Nash equilibrium problem | Constrained equation | Sensitivity | 49J53 | Analysis | 90C33 | Singular solution | 47J05 | COINCIDENCE POINTS | MATHEMATICS, APPLIED | MULTIFUNCTIONS | MAPS | GENERALIZED EQUATIONS | THEOREMS | CONE | Game theory

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 9/2017, Volume 75, Issue 1, pp. 114 - 127

In this paper we consider the nonlinear system $$\gamma _i(x_i)=\sum _{j=1}^{m}g_{ij} (x_j)$$ γ i ( x i ) = ∑ j = 1 m g i j ( x j ) , $$ 1\le i \le m$$ 1 ≤ i ≤...

Nonlinear algebraic system | Positive solution | Uniqueness | Mathematics, general | Mathematics | 47J05 | Existence | MATHEMATICS | MATHEMATICS, APPLIED | NEURAL-NETWORKS | STABILITY | COMPARTMENTAL-SYSTEMS | QUALITATIVE THEORY | PIPES | PARAMETER

Nonlinear algebraic system | Positive solution | Uniqueness | Mathematics, general | Mathematics | 47J05 | Existence | MATHEMATICS | MATHEMATICS, APPLIED | NEURAL-NETWORKS | STABILITY | COMPARTMENTAL-SYSTEMS | QUALITATIVE THEORY | PIPES | PARAMETER

Journal Article

Acta Mathematica Vietnamica, ISSN 0251-4184, 3/2016, Volume 41, Issue 1, pp. 55 - 68

We consider a regularization method based on the Browder–Tikhonov and iterative regularization method that can be used to find a solution of a class of...

Variational inequality | Accretive mapping | 47H09 | Mathematics, general | Mathematics | 47J05 | 47J06 | Regularization | 47H06 | Nonexpansive mapping | Fixed point

Variational inequality | Accretive mapping | 47H09 | Mathematics, general | Mathematics | 47J05 | 47J06 | Regularization | 47H06 | Nonexpansive mapping | Fixed point

Journal Article