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Structural Fixed Point Results in Metric Spaces

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Mathematical Analysis, Approximation Theory and Their Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 111))

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Abstract

In Part 1, a class of anticipative contractions over quasi-ordered metric spaces is introduced and a corresponding lot of metrical fixed point theorems is formulated. The obtained facts include some well-known statements in the area due to Boyd and Wong or Matkowski, as well as a recent contribution due to Choudhury and Kundu (Demonstr Math 46:327–334, 2013). Further, in Part 2, a relative type version is given for the fixed point result in Leader (Math Jpn 24:17–24, 1979). Finally, in Part 3, an almost metric version is established for the 2008 Jachymski fixed point result (Proc Am Math Soc 136:1359–1373, 2008) involving Banach contractions over metric spaces endowed with a graph.

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Turinici, M. (2016). Structural Fixed Point Results in Metric Spaces. In: Rassias, T., Gupta, V. (eds) Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-31281-1_28

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