Bhatt, Arvind; Chandra, Harish; Sahu, D. R. Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions. (English) Zbl 1227.47034 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 176-182 (2010). The authors establish several common fixed point theorems for two maps and four maps without using the (E.A.) property and completeness, under a relaxed condition on \(d\), without using the the triangle inequality and assuming symmetry only on the set of points of coincidence. An application to dynamical programming is also given. Reviewer: Long Wei (Jiangxi) Cited in 5 ReviewsCited in 18 Documents MSC: 47H10 Fixed-point theorems 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:common fixed point; occasionally weakly compatible; triangle inequality PDF BibTeX XML Cite \textit{A. Bhatt} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 1, 176--182 (2010; Zbl 1227.47034) Full Text: DOI OpenURL References: [1] Kannan, R., Some results on fixed points, Bull. Calcutta math. soc., 60, 71-76, (1968) · Zbl 0209.27104 [2] Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. inst. math., 32, 149-153, (1982) · Zbl 0523.54030 [3] Jungck, G., Compatible mappings and common fixed points, Int. J. math. math. sci., 9, 771-779, (1986) · Zbl 0613.54029 [4] Pant, R.P., Common fixed points of four maps, Bull. Calcutta math. soc., 90, 281-286, (1998) · Zbl 0936.54043 [5] Aamri, M.; El Moutawakil, D., Some new common fixed point theorems under strict contractive conditions, J. math. anal. appl., 270, 181-188, (2002) · Zbl 1008.54030 [6] Al-Thagafi, M.A.; Shahzad, Naseer, Generalized I-nonexpansive selfmaps and invariant approximations, Acta math. sinica, 24, 867-876, (2008) · Zbl 1175.41026 [7] Jungck, G., Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far east J. math. sci., 4, 19-215, (1996) · Zbl 0928.54043 [8] Jungck, G.; Rhoades, B.E., Fixed point theorems for occasionally weakly compatible mappings, Fixed point theory, 7, 286-296, (2006) · Zbl 1118.47045 [9] Jungck, G.; Rhoades, B.E., Fixed point theorems for occasionally weakly compatible mappings, Fixed point theory, 9, 383-384, (2008), (Erratum) · Zbl 1118.47045 [10] Bellman, B.; Lee, E.S., Functional equation arising in dynamic programming, Aequationes math., 17, 1-18, (1979) 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.