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An integral type fixed point theorem for multi-valued mappings employing strongly tangential property. (English) Zbl 1490.54045

Summary: W. Sintunavarat and P. Kumam [Int. J. Math. Math. Sci. 2011, Article ID 923458, 12 p. (2011; Zbl 1215.54026)] extended the tangential property to hybrid pair of mappings which generalizes the idea of tangential property due to H. K. Pathak and N. Shahzad [Bull. Belg. Math. Soc. - Simon Stevin 16, No. 2, 277–288 (2009; Zbl 1167.54016)]. In the present paper, we introduce the notion of strong tangential property and utilize the same to prove an integral type metrical common fixed point theorem for non-self mappings. An illustrative example is also furnished to support our main result. Our results are corrected, improved and generalized versions of a multitude of relevant common fixed point theorems of the existing literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54C60 Set-valued maps in general topology
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