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Common fixed point theorems for six mappings with some weaker conditions in 2-metric spaces
Faculty
Science
Year:
2012
Type of Publication:
Article
Pages:
99-112
Authors:
Abd-Rabou, Khaled
Journal:
KUWAIT JOURNAL OF SCIENCE \& ENGINEERING ACADEMIC PUBLICATION COUNCIL
Volume:
39
Research Area:
Science \& Technology - Other Topics
ISSN
ISI:000307319000006
Keywords :
Common fixed point, single and set-valued mappings, weak commutativity of type (Kh)
Abstract:
In this paper, we prove unique common fixed-point theorems for six mappings (two set-valued and four single-valued mappings) without assuming compatibility and continuity of any mapping on noncomplete 2-metric spaces. To prove these theorems, we introduce a noncompatible condition, that is, weak commutativity of type (Kh) in a 2-metric space. We show that completeness of the whole space is not necessary for the existence and uniqueness of common fixed point. Also, we prove common fixed point theorems for two self mappings and two sequences set-valued mappings by the same weaker conditions. Our results improve, extend and generalize the corresponding results given by many authors.
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