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Invariant approximation for CAT(0) spaces. (English) Zbl 1188.54022

In the year 2008, T. Suzuki [J. Math. Anal. Appl. 340, No. 2, 1088–1095 (2008; Zbl 1140.47041)] showed the following:

Let T be a mapping on a subset C of a Banach space E. Then T is said to satify condition (C) if

(1/2)x-Txx-y,

for all x,yC. In this paper, the authors apply this to the solution of the problem for commuting pairs consisting of a single valued mapping and a multivalued mapping in CAT(0) spaces. For this a multivalued version of condition (C) in CAT(0) spaces has been defined.

In this way the authors improve and extend the results of N. Shahzad and J. Markin, in [J. Math. Anal. Appl. 337, No. 2, 1457–1464 (2008; Zbl 1137.47043)].


MSC:
54H25Fixed-point and coincidence theorems in topological spaces
41A50Best approximation, Chebyshev systems
47H10Fixed point theorems for nonlinear operators on topological linear spaces