D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 52 Citations 15,168 143 World Ranking 487 National Ranking 24

Overview

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.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Iterative Algorithms for Nonlinear Operators

Hong-Kun Xu.
Journal of The London Mathematical Society-second Series (2002)

1922 Citations

VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS

Hong Kun Xu.
Journal of Mathematical Analysis and Applications (2004)

1201 Citations

Inequalities in Banach spaces with applications

Hong-Kun Xu.
Nonlinear Analysis-theory Methods & Applications (1991)

1177 Citations

Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process

Kok-Keong Tan;Hong-Kun Xu.
Journal of Mathematical Analysis and Applications (1993)

1058 Citations

An Iterative Approach to Quadratic Optimization

H K Xu.
Journal of Optimization Theory and Applications (2003)

827 Citations

WEAK AND STRONG CONVERGENCE THEOREMS FOR STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACES

Giuseppe Marino;Hong-Kun Xu.
Journal of Mathematical Analysis and Applications (2007)

673 Citations

A general iterative method for nonexpansive mappings in Hilbert spaces

Giuseppe Marino;Hong-Kun Xu.
Journal of Mathematical Analysis and Applications (2006)

628 Citations

Strong convergence of the CQ method for fixed point iteration processes

Carlos Martinez-Yanes;Hong-Kun Xu.
Nonlinear Analysis-theory Methods & Applications (2006)

412 Citations

Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

H. K. Xu;T. H. Kim.
Journal of Optimization Theory and Applications (2003)

387 Citations

AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS

Hong-Kun Xu;Ramesh G. Ori.
Numerical Functional Analysis and Optimization (2001)

352 Citations

Best Scientists Citing Hong-Kun Xu

Jen-Chih Yao

Jen-Chih Yao

National Sun Yat-sen University

Publications: 190

Poom Kumam

Poom Kumam

King Mongkut's University of Technology Thonburi

Publications: 189

Yonghong Yao

Yonghong Yao

Tianjin Polytechnic University

Publications: 134

Shin Min Kang

Shin Min Kang

Gyeongsang National University

Publications: 131

Yeol Je Cho

Yeol Je Cho

Gyeongsang National University

Publications: 126

Xiaolong Qin

Xiaolong Qin

Hangzhou Normal University

Publications: 101

Naseer Shahzad

Naseer Shahzad

King Abdulaziz University

Publications: 75

Wataru Takahashi

Wataru Takahashi

Tokyo Institute of Technology

Publications: 74

Charles E. Chidume

Charles E. Chidume

African Institute of Science and Technology

Publications: 73

Qamrul Hasan Ansari

Qamrul Hasan Ansari

Aligarh Muslim University

Publications: 66

Ravi P. Agarwal

Ravi P. Agarwal

Texas A&M University – Kingsville

Publications: 48

Muhammad Aslam Noor

Muhammad Aslam Noor

COMSATS University Islamabad

Publications: 36

Mohamed A. Khamsi

Mohamed A. Khamsi

The University of Texas at El Paso

Publications: 36

Simeon Reich

Simeon Reich

Technion – Israel Institute of Technology

Publications: 26

Nawab Hussain

Nawab Hussain

King Abdulaziz University

Publications: 25

Mujahid Abbas

Mujahid Abbas

University of Pretoria

Publications: 19

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

If you think any of the details on this page are incorrect, let us know.

Contact us
Something went wrong. Please try again later.