Common fixed point theorems for weakly compatible quasi contraction mappings

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Defin...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2006-12, Vol.113 (4), p.257-267
Main Authors: Ćirić, Lj. B., Nikolić, N. T., Ume, J. S.
Format: Article
Language:English
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Summary:Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ciric and Rhoades and Watson.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-006-0103-z