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On set-valued contractions of Nadler type in cone metric spaces. (English) Zbl 1206.54067
Summary: The fixed point theory for cone metric spaces, which was introduced in 2007 by L.-G. Huang and X. Zhang [in J. Math. Anal. Appl. 332, No. 2, 1467–1475 (2007; Zbl 1118.54022)] has recently become a subject of interest for many authors. Cone metric spaces are generalizations of metric spaces where the metric is replaced by a mapping d:M×ME, where M, and E is a real Banach space. In the present paper for a cone metric space (M,d) and for a family 𝒜 of subsets of M we establish a new cone metric H:𝒜×𝒜E. Next, we introduce the concept of set-valued contraction of Nadler type and prove a fixed point theorem. Examples are provided.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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