research
Fumiaki Kohsaka
Research Fields
Convex analysis, Nonlinear analysis, Fixed point theory, Optimization theory
Keywords
Convex minimization problem, minimax problem, fixed point theorem, proximal point algorithm, subdifferential, monotone operator, accretive operator, Hilbert space, Banach space, Hadamard space, geodesic metric space
Research Interests
I have been working on fixed point theory and its applications to nonlinear problems in Hilbert spaces, Banach spaces, and geodesic metric spaces. I am especially interested in the asymptotic behavior of sequences generated by the proximal point algorithm and its modifications for maximal monotone operators in Banach spaces. I am also trying to find a class of nonlinear operators which is suitable for the study of the zero point problem for monotone operators in Banach spaces.
The topics can be classified as follows:
Modified proximal point algorithm for accretive operators in Banach spaces
Convex minimization theorem, Takahashi's nonconvex minimization theorem, and Bishop-Phelps' theorem
Proximal point algorithm and its modifications for monotone operators in Banach spaces
Projection methods for convex feasibility problems in Banach spaces
Approximation of fixed points of relatively nonexpansive mappings in Banach spaces
On the set of common fixed points of a countable family of relatively nonexpansive mappings in Banach spaces
On the existence of fixed points of nonspreading mappings and firmly nonexpansive-type mappings in Banach spaces
Approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces
Generalizations of firmly nonexpansive mappings and their relation to monotone operator theory
On the existence of a common fixed point of noncommutative semigroups of nonexpansive mappings in compact convex metric spaces
Existence and approximation of fixed points of firmly nonexpansive mappings in Hilbert spaces
Existence and approximation of minimizers of convex functions in geodesic metric spaces