Monotone Vector Fields and Generation of Nonexpansive Semigroups in Complete CAT(0) Spaces

References

• Jost, J. (1995). Convex functionals and generalized harmonic maps into spaces of nonpositive curvature. Comment. Math. Helv. 70(1):659–673. DOI: 10.1007/BF02566027.
   Web of Science ®Google Scholar
• Mayer, U. F. (1998). Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom. 6(2):199–253. DOI: 10.4310/CAG.1998.v6.n2.a1.
   Web of Science ®Google Scholar
• Bačák, M. (2013). The proximal point algorithm in metric spaces. Isr. J. Math. 194(2):689–701. DOI: 10.1007/s11856-012-0091-3.
   Web of Science ®Google Scholar
• Bačák, M. (2014). Convex Analysis and Optimization in Hadamard Spaces, Volume 22 of De Gruyter Series in Nonlinear Analysis and Applications. Berlin: De Gruyter.
   Google Scholar
• Khatibzadeh, H., Ranjbar, S. (2017). Monotone operators and the proximal point algorithm in complete Cat(0) metric spaces. J. Aust. Math. Soc. 103(1):70–90.
   Web of Science ®Google Scholar
• Chaipunya, P., Kumam, P. (2017). On the proximal point method in Hadamard spaces. Optimization. 66(10):1647–1665. DOI: 10.1080/02331934.2017.1349124.
   Web of Science ®Google Scholar
• Kakavandi, B. A., Amini, M. (2010). Duality and subdifferential for convex functions on complete CAT(0) metric spaces. Nonlinear Anal. 73(10):3450–3455.
   Web of Science ®Google Scholar
• Kakavandi, B. A. (2013). Weak topologies in complete CAT(0) metric spaces. Proc. Amer. Math. Soc. 141(3):1029–1039.
   Web of Science ®Google Scholar
• Németh, S. Z. (1999). Monotone vector fields. Publ. Math. Debrecen. 54(3-4):437–449.
   Web of Science ®Google Scholar
• Li, C., López, G., Martín-Márquez, V. (2009). Monotone vector fields and the proximal point algorithm on Hadamard manifolds. J. Lond. Math. Soc. (2). 79(3):663–683. DOI: 10.1112/jlms/jdn087.
   Web of Science ®Google Scholar
• Nikolaev, I. (1995). The tangent cone of an Aleksandrov space of curvature ≤K. Manuscripta Math. 86(2):137–147.
   Web of Science ®Google Scholar
• Jost, J. (1998). Nonlinear Dirichlet forms. In New Directions in Dirichlet Forms, Volume 8 of AMS/IP Stud. Adv. Math.. Providence, RI: Amer. Math. Soc, pp. 1–47.
   Google Scholar
• Stojkovic, I. (2012). Approximation for convex functionals on non-positively curved spaces and the Trotter-Kato product formula. Adv. Calc. Var. 5(1):77–126. DOI: 10.1515/acv.2011.011.
   Web of Science ®Google Scholar
• Iwamiya, T., Okochi, H. (2003). Monotonicity, resolvents and Yosida approximations of operators on Hilbert manifolds. Nonlinear Anal. 54(2):205–214. DOI: 10.1016/S0362-546X(03)00040-3.
   Web of Science ®Google Scholar
• Wang, J. H., López, G., Martín-Márquez, V., Li, C. (2010). Monotone and accretive vector fields on Riemannian manifolds. J. Optim. Theory Appl. 146(3):691–708. DOI: 10.1007/s10957-010-9688-z.
   Web of Science ®Google Scholar
• Dhompongsa, S., Kirk, W. A., Sims, B. (2006). Fixed points of uniformly Lipschitzian mappings. Nonlinear Anal. 65(4):762–772. DOI: 10.1016/j.na.2005.09.044.
   Web of Science ®Google Scholar
• Kirk, W. A., Panyanak, B. (2008). A concept of convergence in geodesic spaces. Nonlinear Anal. 68(12):3689–3696. DOI: 10.1016/j.na.2007.04.011.
   Web of Science ®Google Scholar
• Kimura, Y. (2010). Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball. Abstr. Appl. Anal. 2010:1–11. DOI: 10.1155/2010/582475.
   Google Scholar
• Bridson, M. R., Haefliger, A. (1999). Metric Spaces of Non-Positive Curvature, Volume 319 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag.
   Google Scholar
• Burago, D., Burago, Y., Ivanov, S. (2001). A Course in Metric Geometry, Volume 33 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.
   Google Scholar
• Ariza-Ruiz, D., Leuştean, L., López-Acedo, G. (2014). Firmly nonexpansive mappings in classes of geodesic spaces. Trans. Amer. Math. Soc. 366(8):4299–4322. DOI: 10.1090/S0002-9947-2014-05968-0.
   Web of Science ®Google Scholar
• Nicolae, A. (2013). Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces, Nonlinear Anal. 87:102–115.
   Google Scholar
• Banert, S. (2014). Backward-backward splitting in Hadamard spaces. J. Math. Anal. Appl. 414(2):656–665. DOI: 10.1016/j.jmaa.2014.01.054.
   Web of Science ®Google Scholar
• Yosida, K. (1995). Functional Analysis. Classics in Mathematics. Berlin: Springer-Verlag, Reprint of the sixth (1980) edition.
   Google Scholar
• Kōmura, Y., Konishi, Y. (1983). Hisenkei Hatten Hoteishiki, Volume 16 of Iwanami Shoten Kiso Sūgaku [Iwanami Lectures on Fundamental Mathematics]. Tokyo: Iwanami Shoten, second edition, Kaisekigaku (II) [Analysis (II)], vii.
   Google Scholar
• Crandall, M. G., Liggett, T. M. (1971). Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93(2):265–298. DOI: 10.2307/2373376.
   Web of Science ®Google Scholar