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Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces. (English) Zbl 1205.47051
Summary: In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of {\it S. Dhompongsa, A. Kaewcharoen} and {\it A. Kaewkhao} [Nonlinear Anal., Theory Methods Appl. 64, No. 5 (A), 958--970 (2006; Zbl 1106.47046)]. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly $L(\tau)$ spaces; our result generalizes a recent result of {\it T. Domínguez-Benavides, J. García-Falset, E. Llorens-Fuster} and {\it P. Lorenzo-Ramírez} [Nonlinear Anal., Theory Methods Appl. 71, No.  5--6 (A), 1562--1571 (2009; Zbl 1181.47055)].

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
47H04Set-valued operators
Full Text: DOI EuDML