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Fixed point theory for generalized $$\varphi$$-weak contractions. (English) Zbl 1163.47304
Summary: Fixed point and coincidence results are presented for single-valued hybrid generalized $$\varphi$$-weak contractions $$T,S$$ defined on complete metric spaces.

##### MSC:
 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 54H25 Fixed-point and coincidence theorems (topological aspects)
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##### References:
 [1] Alber, Ya.I.; Guerre-Delabriere, S., Principles of weakly contractive maps in Hilbert spaces, (), 7-22 · Zbl 0897.47044 [2] Al-Thagafi, M.A.; Shahzad, N., Noncommuting selfmaps and invariant approximations, Nonlinear anal., 64, 2778-2786, (2006) · Zbl 1108.41025 [3] Boyd, D.W.; Wong, T.S.W., On nonlinear contractions, Proc. amer. math. soc., 20, 458-464, (1969) · Zbl 0175.44903 [4] Hussain, N.; Jungck, G., Common fixed point and invariant approximation results for noncommuting generalized $$(f, g)$$-nonexpansive maps, J. math. anal. appl., 321, 851-861, (2006) · Zbl 1106.47048 [5] Reich, S., Some fixed point problems, Atti. accad. naz. lincei, 57, 194-198, (1974) · Zbl 0329.47019 [6] Rhoades, B.E., Some theorems on weakly contractive maps, Nonlinear anal., 47, 2683-2693, (2001) · Zbl 1042.47521 [7] Shahzad, N., Invariant approximations, generalized I-contractions, and $$R$$-subweakly commuting maps, Fixed point theory appl., 1, 79-86, (2005) · Zbl 1083.54540 [8] Song, Y., Coincidence points for noncommuting $$f$$-weakly contractive mappings, Int. J. comput. appl. math. (IJCAM), 2, 1, 51-57, (2007) · Zbl 1256.54083 [9] Song, Y., Common fixed points and invariant approximations for generalized $$(f, g)$$-nonexpansive mappings, Commun. math. anal., 2, 17-26, (2007) · Zbl 1168.41312 [10] Song, Y.; Xu, S., A note on common fixed-points for Banach operator pairs, Int. J. contemp. math. sci., 2, 1163-1166, (2007) · Zbl 1151.41311
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