On nonspreading-type mappings in Hadamard spaces
Resumo
In this paper, we studied a new class of nonspreading-type mappings more general than the class of strictly pseudononspreading and the class of generalized nonspreading mappings. We state and prove some strong convergence theorems of the Mann-type and Ishikawa-type algorithms for approximating fixed points of our class of mappings in Hadamard spaces.
Downloads
Referências
I. D. Berg and I. G. Nikolaev, Quasilinearization and curvature of Alexandrov spaces, Geom. Dedicata, 133 (2008), 195-218.
M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Fundamental Principle of Mathematical Sciences, Springer, Berlin, Germany, 319 (1999).
F. Bruhat and J. Tits, Groupes Reductifs sur un Corp Local, I. Donnees Radicielles Valuees, Institut des Hautes Etudes Scientifiques, 41 (1972).
H. Dehghan and J. Rooin, Metric projection and convergence theorems for nonexpansive mapping in Hadamard spaces, arXiv:1410.1137VI [math.FA], 5 Oct. (2014).
S. Dhompongsa, W. A. Kirk and B. Sims, Fixed points of uniformly Lipschitzian mappings, Nonlinear Anal., 64(4) (2006), 762-772.
S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45.
S. Dhompongsa and B. Panyanak, On -convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008), 2572-2579.
K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, Marcel Dekker, New York, (1984).
B. A. Kakavandi and M. Amini, Duality and subdifferential for convex functions on complete CAT(0) metric spaces, Nonlinear Anal., 73(2010), 3450-3455.
W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), 3689-3696.
F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math., 91 (2008), 166-177.
T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60 (1976), 179-182.
P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912.
B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 2010, Article ID 268780, 2010, 14 pages.
E. Naraghirad, On an open question of Takahashi for nonspreading mappings in Banach spaces, Fixed Point Theory Appl., 2013, 2013:228.
F. U Ogbuisi and O. T. Mewomo, Iterative solution of split variational inclusion problem in real Banach space, Afr. Mat, 28 (2017), 295-309.
C. C. Okeke, A. U. Bello, C. Izuchukwu and O.T. Mewomo, Split equality for monotone inclusion problem and fixed point problem in real Banach spaces, Aust. J. Math. Anal. Appl, 14 (2)(2018), 1-20.
M. O. Osilike and F. O. Isiogugu, Weak and strong convergence theorems for nonspreading-type mappings in Hilbert spaces, Nonlinear Anal., 74 (2011), 1814-1822.
W. Phuengrattana, On the generalized asymptotically nonspreading mappings in convex metric spaces, Appl. Gen. Topol., 18(1) (2017), 117-129.
S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal., 15 (1990), 537-558.
H. K. Xu, Iterative algorithms for nonlinear operators, J. London. Math. Soc., 2 (2002), 240-256.
Copyright (c) 2020 Boletim da Sociedade Paranaense de Matemática

This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).