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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 S. Dhompongsa, A. Kaewcharoen and 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 $L\left(\tau \right)$ spaces; our result generalizes a recent result of T. Domínguez-Benavides, J. García-Falset, E. Llorens-Fuster and P. Lorenzo-Ramírez [Nonlinear Anal., Theory Methods Appl. 71, No.  5–6 (A), 1562–1571 (2009; Zbl 1181.47055)].
MSC:
 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47H09 Mappings defined by “shrinking” properties 47H04 Set-valued operators
References:
 [1] [2] [3] [4] [5] [6]