7 papers
The proximal point method and its two variants for monotone vector fields in Hadamard spaces
Parin Chaipunya, Fumiaki Kohsaka
We prove existence and convergence of sequences generated by the proximal point method and its two variants for monotone vector fields in Hadamard spaces. Before obtaining our resu…
Sion's minimax theorem and the proximal point algorithm in Hadamard spaces
Fumiaki Kohsaka
We obtain Sion's minimax theorem in Hadamard spaces and discuss its applications. Among other things, we study several fundamental properties of resolvents of saddle functions in H…
Monotone vector fields and generation of nonexpansive semigroups in complete CAT(0) spaces
Parin Chaipunya, Fumiaki Kohsaka, Poom Kumam
In this paper, we discuss about monotone vector fields, which is a typical extension to the theory of convex functions, by exploiting the tangent space structure. This new approach…
Fixed points of metrically nonspreading mappings in Hadamard spaces
Fumiaki Kohsaka
We study the existence and approximation of fixed points of metrically nonspreading mappings and firmly metrically nonspreading mappings in Hadamard spaces. The resolvents of monot…
The proximal point algorithm in geodesic spaces with curvature bounded above
Yasunori Kimura, Fumiaki Kohsaka
We investigate the asymptotic behavior of sequences generated by the proximal point algorithm for convex functions in complete geodesic spaces with curvature bounded above. Using t…
Existence and approximation of fixed points of vicinal mappings in geodesic spaces
Fumiaki Kohsaka
We propose the concepts of vicinal mappings and firmly vicinal mappings in metric spaces. We obtain fixed point and convergence theorems for these mappings in complete geodesic spa…