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Nonlinear Functional Analysis and Convex Analysis Lab (Ibaraki)
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The lab theoretically explores how to approach fixed points of nonlinear mappings.
AboutAbout the lab
Capturing fixed points of mappings through approximation methods.
In this lab, Professor Ibaraki studies fixed point problems for nonlinear mappings in Hilbert spaces and Banach spaces.
Research on fixed point problems rests on two pillars, existence and approximation methods, and the nonexpansiveness of the mapping is a key factor.
The lab proposes approximation methods that construct a sequence of points step by step toward a solution, and has obtained theorems showing that the sequence converges to the solution.
According to the researcher directory, in the 2026 academic year Professor Ibaraki is in charge of graduation research for the Faculty of Education.
Key terms
- Zero point problem
- The problem of finding a zero point of a maximal monotone operator. It generalizes many nonlinear problems, such as convex optimization problems and equilibrium problems.
- Proximal point algorithm
- A representative approximation method for approaching a solution of the zero point problem. It builds a sequence of points step by step using a mapping called the resolvent operator.
ResearchResearch themes
The lab studies fixed point problems for nonlinear mappings in Banach spaces and Hilbert spaces. It develops theory from two sides: approximation methods for fixed points, and the proximal point algorithm for solving the zero point problem of maximal monotone operators.
Fixed Point Problems from the Viewpoint of Attractive Points
The lab is building a theory that re-examines fixed point problems for nonlinear mappings in Banach spaces from the new viewpoint of attractive points. In Hilbert spaces, it has proposed new approximation methods for common attractive fixed points of two nonlinear mappings and obtained strong convergence theorems.
Zero Point Problem for Maximal Monotone Operators
The lab studied algorithms for computing values of the resolvent operator used in the proximal point algorithm. It also obtained results on approximation methods for fixed points of various nonexpansive-type mappings in Banach spaces and Hilbert spaces.
MembersFaculty
- ProfessorTakanori Ibaraki
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