# zbMATH — the first resource for mathematics

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)
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.