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Pair of non-self-mappings and common fixed points. (English) Zbl 1118.54304

Authors’ abstract: We study quasi-contraction type non-self-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Imdad and Kumar, Das and Naik, Jungck, Ćirić, Ume, Khan and Pathak, and Ćirić are established.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Assad, N. A.; Kirk, W. A., Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math., 43, 553-562 (1972) · Zbl 0239.54032
[2] Berinde, V., Approximation of fixed points of some nonself generalized \(ϕ\)-contractions, Math. Balk., 18, 85-93 (2004) · Zbl 1083.54530
[3] Ćirić, Lj. B., A generalization of Bahach’s contraction principle, Proc. Am. Math. Soc., 45, 267-273 (1974) · Zbl 0291.54056
[4] Ćirić, Lj. B., Quasi contraction nonself mapping on Banach spaces, Bull. Acad. Serbe Sci. Arts, Cl. Sci. Math. Natur. Sci. Math., 23, 25-31 (1998) · Zbl 1261.47070
[5] Ćirić, Lj. B.; Ume, J. S.; Khan, M. S.; Pathak, H. K., On some non-self mappings, Math. Nach., 251, 28-33 (2003) · Zbl 1024.47033
[6] Ćirić, Lj. B., Contractive type non-self mappings on metric spaces of hyperbolic type, J. Math. Anal. Appl, 317, 28-42 (2006) · Zbl 1089.54019
[7] Das, K. M.; Naik, K. V., Common fixed point theorems for commuting maps on metric space, Proc. Am. Math. Soc., 77, 369-373 (1979) · Zbl 0418.54025
[8] Gajić, Lj., Quasi-contractive nonself mappings on Takahashi convex metric spaces, Novi Sad J. Math., 30, 41-46 (2000)
[9] Gajić, Lj.; Rakočević, V., Quasi contractive nonself mappings on convex metric spaces and common fixed point theorems, Fixed Point Theory Appl., 3, 365-375 (2005) · Zbl 1104.54018
[10] Imdad, M.; Kumar, S., Rhoades-type fixed-point theorems for a pair of nonself mappings, Comput. Math. Appl., 46, 919-927 (2003) · Zbl 1065.47059
[11] Jungck, G., Commuting maps and fixed, points, Am. Math. Monthly, 83, 261-263 (1976) · Zbl 0321.54025
[12] Rakočević, V., Functional Analysis (1994), Naucna knjiga: Naucna knjiga Beograd
[13] Rakočević, V., Quasi contraction nonself mappings on Banach spaces and common fixed point theorem, Publ. Math. Debrecen, 58, 451-460 (2001) · Zbl 0980.46037
[14] Rhoades, B. E., A fixed point theorem for non-self mappings, Math. Japon., 23, 457-459 (1978) · Zbl 0396.47038
[15] Sessa, S., On weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beagrad), 32, 46, 149-153 (1982) · Zbl 0523.54030
[16] Takahashi, W., A convexity in metric space and nonexpansive mappings, I. Kodai Math. Sem. Pep., 22, 142-149 (1970) · Zbl 0268.54048
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