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Hybrid fixed point theorems in symmetric spaces via common limit range property. (English) Zbl 1304.54081

Summary: In this paper, we point out that some recent results of Y. K. Vijaywar et al. [Demonstr. Math. 45, No. 3, 611–620 (2012; Zbl 1290.54027)] are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Citations:

Zbl 1290.54027
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Full Text: DOI

References:

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