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The existence of fixed points for nonlinear contractive maps in metric spaces with \(w\)-distances. (English) Zbl 1235.54044
Summary: Some fixed point theorems for \((\varphi, \psi, p)\)-contractive maps and \((\varphi, k, p)\)-contractive maps on a complete metric space are proved. Presented fixed point theorems generalize many results existing in the literature.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, pp. 531-536, 2002. · Zbl 0993.54040
[2] O. Kada, T. Suzuki, and W. Takahashi, “Nonconvex minimization theorems and fixed point theorems in complete metric spaces,” Mathematica Japonica, vol. 44, no. 2, pp. 381-391, 1996. · Zbl 0897.54029
[3] A. Razani, Z. Mazlumi Nezhad, and M. Boujary, “A fixed point theorem for w-distance,” Applied Sciences, vol. 11, pp. 114-117, 2009. · Zbl 1184.54043
[4] T. Suzuki and W. Takahashi, “Fixed point theorems and characterizations of metric completeness,” Topological Methods in Nonlinear Analysis, vol. 8, no. 2, pp. 371-382, 1996. · Zbl 0902.47050
[5] W.-S. Du, “Fixed point theorems for generalized Hausdorff metrics,” International Mathematical Forum, vol. 3, no. 21-24, pp. 1011-1022, 2008. · Zbl 1158.54020
[6] T. L. Hicks and B. E. Rhoades, “A Banach type fixed-point theorem,” Mathematica Japonica, vol. 24, no. 3, pp. 327-330, 1979/80. · Zbl 0432.47036
[7] B. E. Rhoades and M. Abbas, “Maps satisfying generalized contractive conditions of integral type for which F(T)=F(Tn),” International Journal of Pure and Applied Mathematics, vol. 45, no. 2, pp. 225-231, 2008. · Zbl 1161.54024
[8] G. S. Jeong and B. E. Rhoades, “Maps for which F(T)=F(Tn),” Fixed Point Theory and Applications, vol. 6, pp. 87-131, 2005.
[9] H. Lakzian and B. E. Rhoades, “Maps satisfying generalized contractive contractions of integral type for which F(T)=F(Tn),” submitted to International Journal of Pure and Applied Mathematical Sciences.
[10] R. Kannan, “Some results on fixed points. II,” The American Mathematical Monthly, vol. 76, pp. 405-408, 1969. · Zbl 0179.28203
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