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A note on tvs-cone metric fixed point theory. (English) Zbl 1237.54058

Summary: The concept of set-valued contraction of Nadler type in the setting of tvs-cone spaces is introduced and a fixed point theorem in the setting of tvs-cone spaces with respect to a solid cone is proved. The obtained results extend and generalize the main results of [S. B. Nadler jun\., Pac. J. Math. 30, 475–488 (1969; Zbl 0187.45002)] and [D. Wardowski, Appl. Math. Lett. 24, No. 3, 275–278 (2011; Zbl 1206.54067)]. Two examples are given to illustrate the usability of the results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
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References:

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