What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Hilbert space
- Topology
His main research concerns Hilbert space, Mathematical analysis, Fixed point, Iterative method and Algorithm.
His Hilbert space research includes themes of Fixed-point iteration, Weak convergence, Common fixed point, Iteration process and Applied mathematics.
Hong-Kun Xu studies Banach space, a branch of Mathematical analysis.
His study in Fixed point is interdisciplinary in nature, drawing from both Discrete mathematics, Fixed-point theorem, Norm and Variational inequality, Mathematical optimization.
Proof mining, Nonlinear operators, Local convergence and Quadratic programming is closely connected to Quadratic equation in his research, which is encompassed under the umbrella topic of Iterative method.
His Algorithm research is multidisciplinary, incorporating elements of Minimization problem and Convex optimization.
His most cited work include:
- Iterative Algorithms for Nonlinear Operators (1201 citations)
- VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS (760 citations)
- Inequalities in Banach spaces with applications (684 citations)
What are the main themes of his work throughout his whole career to date?
Hong-Kun Xu mainly focuses on Mathematical analysis, Fixed point, Banach space, Discrete mathematics and Hilbert space.
Hong-Kun Xu interconnects Applied mathematics, Pure mathematics and Combinatorics in the investigation of issues within Mathematical analysis.
His Fixed point study combines topics in areas such as Semigroup, Intersection and Convex optimization.
His study focuses on the intersection of Banach space and fields such as Bounded function with connections in the field of Hausdorff distance.
Hong-Kun Xu has researched Discrete mathematics in several fields, including Ergodic theory and Contraction.
Hong-Kun Xu combines subjects such as Projection, Weak convergence, Iterative method, Algorithm and Midpoint method with his study of Hilbert space.
He most often published in these fields:
- Mathematical analysis (62.50%)
- Fixed point (45.39%)
- Banach space (39.47%)
What were the highlights of his more recent work (between 2010-2021)?
- Mathematical analysis (62.50%)
- Hilbert space (31.58%)
- Iterative method (25.66%)
In recent papers he was focusing on the following fields of study:
His primary areas of investigation include Mathematical analysis, Hilbert space, Iterative method, Applied mathematics and Mathematical optimization.
The Mathematical analysis study combines topics in areas such as Pure mathematics and Convex optimization.
His Hilbert space research is multidisciplinary, incorporating perspectives in Projection, Weak convergence, Midpoint method, Algorithm and Sequence.
The various areas that Hong-Kun Xu examines in his Iterative method study include Norm, Competitive Lotka–Volterra equations, Fixed point and Nonlinear diffusion.
His study looks at the intersection of Fixed point and topics like Minimum norm with Projection.
His work on Variational inequality as part of general Applied mathematics research is frequently linked to Logistic function, bridging the gap between disciplines.
Between 2010 and 2021, his most popular works were:
- Averaged Mappings and the Gradient-Projection Algorithm (168 citations)
- Averaged Mappings and the Gradient-Projection Algorithm (168 citations)
- Cyclic algorithms for split feasibility problems in Hilbert spaces (117 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Hilbert space
- Algebra
The scientist’s investigation covers issues in Hilbert space, Mathematical analysis, Applied mathematics, Iterative method and Algorithm.
Mathematical analysis is closely attributed to Weak convergence in his research.
He is interested in Variational inequality, which is a branch of Applied mathematics.
His research in Iterative method intersects with topics in Class, Norm, Common fixed point and Thresholding.
His Algorithm study combines topics from a wide range of disciplines, such as Zero, Bounded function and Limit point.
His Mathematical optimization study integrates concerns from other disciplines, such as Fixed point and Proximal gradient methods for learning.
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