On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition
Articles
Mi Zhou
University of Sanya
Xiao-Lan Liu
Sichuan University of Science and Engineering
Adrian Secelean
Lucian Blaga University of Sibiu
Published 2019-11-07
https://doi.org/10.15388/NA.2019.6.9
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Keywords

coincidence point
common fixed point
common (CLR(AB)(ST)) property
common property (E.A.)
weakly compatible

How to Cite

Zhou M., Liu X.-L. and Secelean A. (2019) “On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition”, Nonlinear Analysis: Modelling and Control, 24(6), pp. 1001–1018. doi: 10.15388/NA.2019.6.9.

Abstract

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

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