Some common fixed point theorems for weakly compatible mappings |
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Authors: | Lj.B. ?iri? J.S. Ume |
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Affiliation: | a Faculty of Mechanical Engineering, Al. Rudara 12-35, 11070 Belgrade, Serbia and Montenegro b Department of Applied Mathematics, Changwon National University, Changwon 641-773, Republic of Korea |
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Abstract: | Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771-779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247-1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] is generalized and improved. |
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Keywords: | Common fixed point Metrically convex metric space |
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