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, Ćirić and Rhoades and Watson.
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This research was financially supported by Changwon National University in 2006.
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Ćirić, L., Nikolić, N. & Ume, J. Common fixed point theorems for weakly compatible quasi contraction mappings. Acta Math Hung 113, 257–267 (2006). https://doi.org/10.1007/s10474-006-0103-z
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DOI: https://doi.org/10.1007/s10474-006-0103-z