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Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces. (English) Zbl 1203.54042
Summary: Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by L.-G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] for cone metric spaces and by D. Klim and D. Wardowski [J. Math. Anal. Appl. 334, No. 1, 132–139 (2007; Zbl 1133.54025)] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
26A18 Iteration of real functions in one variable
Full Text: DOI
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