A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces
Copyright policy )A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces
Abstract In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of f-fixed points of continuous f-pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common f-fixed point of continuous f-pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.
Bregman divergence, 47h05, Economics, 47j05, variational inequality, Fixed-Point Problems, Engineering, Operator space, Nonexpansive Mappings, Monotone operators and generalizations, 47h10, Fixed-point iterations, Variational inequality, Subgradient method, Numerical Analysis, Nonlinear Programming, Numerical Optimization Techniques, Ecology, Physics, Mathematical optimization, Topology Optimization in Structural Engineering, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Computational Theory and Mathematics, monotone mapping, Physical Sciences, Convergence (economics), 47j20, Type (biology), 47j25, Equations involving nonlinear operators (general), 47j26, f-pseudocontractive mapping, Geometry, Mathematical analysis, Quantum mechanics, zero points, Fixed-point theorems, Iterative procedures involving nonlinear operators, QA1-939, FOS: Mathematics, Genetics, semi-pseudocontractive mapping, Biology, Economic growth, Civil and Structural Engineering, Scheme (mathematics), Banach space, \(f\)-pseudocontractive mapping, Semidefinite Programming, Pure mathematics, Fixed point, f-fixed point, Applied mathematics, strong convergence, Variational and other types of inequalities involving nonlinear operators (general), Strongly monotone, Finite-rank operator, FOS: Biological sciences, Computer Science, Nonlinear system, Monotone polygon, Pseudo-monotone operator, \(f\)-fixed point, Mathematics, Mixed-Integer Nonlinear Programs, Sequence (biology)
Bregman divergence, 47h05, Economics, 47j05, variational inequality, Fixed-Point Problems, Engineering, Operator space, Nonexpansive Mappings, Monotone operators and generalizations, 47h10, Fixed-point iterations, Variational inequality, Subgradient method, Numerical Analysis, Nonlinear Programming, Numerical Optimization Techniques, Ecology, Physics, Mathematical optimization, Topology Optimization in Structural Engineering, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Computational Theory and Mathematics, monotone mapping, Physical Sciences, Convergence (economics), 47j20, Type (biology), 47j25, Equations involving nonlinear operators (general), 47j26, f-pseudocontractive mapping, Geometry, Mathematical analysis, Quantum mechanics, zero points, Fixed-point theorems, Iterative procedures involving nonlinear operators, QA1-939, FOS: Mathematics, Genetics, semi-pseudocontractive mapping, Biology, Economic growth, Civil and Structural Engineering, Scheme (mathematics), Banach space, \(f\)-pseudocontractive mapping, Semidefinite Programming, Pure mathematics, Fixed point, f-fixed point, Applied mathematics, strong convergence, Variational and other types of inequalities involving nonlinear operators (general), Strongly monotone, Finite-rank operator, FOS: Biological sciences, Computer Science, Nonlinear system, Monotone polygon, Pseudo-monotone operator, \(f\)-fixed point, Mathematics, Mixed-Integer Nonlinear Programs, Sequence (biology)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!