Common fixed point theorems for weakly compatible quasi contraction mappings |
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| Authors: | Lj. B. &# iri&# , Lj. B. &# iri&# , Lj. B. &# iri&# , N. T. Nikoli&# , N. T. Nikoli&# , N. T. Nikoli&# , Ume J. S., Ume J. S. Ume J. S. |
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| Affiliation: | (1) Faculty of Mechanical Engineering, Al. Rudara 12-35, 11 070 Belgrade, Serbia;(2) Faculty of Mechanical Engineering, Al. Rudara 12-35, 11 070 Belgrade, Serbia;(3) Faculty of Mechanical Engineering, Al. Rudara 12-35, 11 070 Belgrade, Serbia;(4) Faculty of Organizational Science, Jove Ilica 154, 11 000 Belgrade, Serbia;(5) Faculty of Organizational Science, Jove Ilica 154, 11 000 Belgrade, Serbia;(6) Faculty of Organizational Science, Jove Ilica 154, 11 000 Belgrade, Serbia;(7) Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea;(8) Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea;(9) Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea |
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| Abstract: | 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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| Keywords: | weakly compatible mappings stationary point quasi-contraction mapping |
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