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Common fixed point for generalized $$(\psi ,\varphi )$$-weak contractions. (English) Zbl 1203.54040
Summary: We introduce the class of generalized $$(\psi ,\varphi )$$-weak contractive mappings. We establish that these mappings necessarily have a unique common fixed point in complete metric spaces. This result generalizes an existing result in metric spaces.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects)
##### Keywords:
fixed point; generalized contraction; complete metric space
Full Text:
##### References:
 [1] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear analysis, 47, 2683-2693, (2001) · Zbl 1042.47521 [2] Chidume, C.E.; Zegeye, H.; Aneke, S.J., Approximation of fixed points of weakly contractive nonself maps in Banach spaces, Journal of mathematical analysis and applications, 1, 189-199, (2002) · Zbl 1005.47053 [3] Berinde, V., Approximating fixed points of weak $$\varphi$$-contractions, Fixed point theory, 4, 131-142, (2003) · Zbl 1065.47069 [4] Beg, I.; Abbas, M., Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed point theory and applications, 1-7, (2006), Article ID 74503 · Zbl 1133.54024 [5] Mai, J.H.; Liu, X.H., Fixed points of weakly contractive maps and boundedness of orbits, Fixed point theory and applications, (2007), Article ID 20962 · Zbl 1157.54020 [6] Dutta, P.N.; Choudhury, B.S., A generalization of contraction principle in metric spaces, Fixed point theory and applications, 8, (2008), Article ID 406368 · Zbl 1177.54024 [7] Zhang, Q.; Song, Y., Fixed point theory for generalized $$\varphi$$-weak contractions, Applied mathematics letters, 22, 75-78, (2009) · Zbl 1163.47304
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