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Common fixed point theorems under a new continuity condition

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Abstract

The aim of the present paper is to generalize the notion of reciprocal continuity and obtain common fixed point theorems in diverse settings as an application of the new notion. The new notion unifies the approaches of three well known notions- reciprocal continuity, subsequential continuity and conditional commutativity. Our results generalize and extend several fixed point theorems. We also demonstrate that the new notion is a necessary condition for the existence of common fixed points.

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Authors and Affiliations

  1. Department of Mathematics, Kumaun University, D. S. B. Campus, Nainital, 263002, India

    R. P. Pant & R. K. Bisht

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  1. R. P. Pant
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  2. R. K. Bisht
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Correspondence to R. K. Bisht.

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Pant, R.P., Bisht, R.K. Common fixed point theorems under a new continuity condition. Ann Univ Ferrara 58, 127–141 (2012). https://doi.org/10.1007/s11565-011-0141-5

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  • DOI: https://doi.org/10.1007/s11565-011-0141-5

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