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Common fixed point and invariant approximation results for noncommuting generalized $$(f,g)$$-nonexpansive maps. (English) Zbl 1106.47048
Some common fixed point theorems for generalized $$(f,g)$$-nonexpansive $$R$$-subweakly commuting maps are established. As applications, some results on the existence of common fixed points from the set of best approximations are obtained.

##### MSC:
 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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##### References:
 [1] Al-Thagafi, M.A., Common fixed points and best approximation, J. approx. theory, 85, 318-323, (1996) · Zbl 0858.41022 [2] Baskaran, E.; Subrahmanyam, L.V., Common fixed points in closed balls, Atti. sem. mat. fis. univ. modena, 36, 1-5, (1988) · Zbl 0656.54031 [3] Dotson, W.J., Fixed point theorems for nonexpansive mappings on star-shaped subsets of Banach spaces, J. London math. soc., 4, 408-410, (1972) · Zbl 0229.47047 [4] Habiniak, L., Fixed point theorems and invariant approximation, J. approx. theory, 56, 241-244, (1989) · Zbl 0673.41037 [5] Hicks, T.L.; Humphries, M.D., A note on fixed point theorems, J. approx. theory, 34, 221-225, (1982) · Zbl 0483.47039 [6] Hussain, N.; Khan, A.R., Common fixed point results in best approximation theory, Appl. math. lett., 16, 575-580, (2003) · Zbl 1063.47055 [7] N. Hussain, D. O’Regan, R.P. Agarwal, Common fixed point and invariant approximation results on non-star-shaped domain, Georgian Math. J., in press [8] Jungck, G., Common fixed points for commuting and compatible maps on compacta, Proc. amer. math. soc., 103, 977-983, (1988) · Zbl 0661.54043 [9] Jungck, G.; Sessa, S., Fixed point theorems in best approximation theory, Math. japon., 42, 249-252, (1995) · Zbl 0834.54026 [10] Meinardus, G., Invarianze bei linearen approximationen, Arch. ration. mech. anal., 14, 301-303, (1963) · Zbl 0122.30801 [11] Pathak, H.K.; Khan, M.S., Fixed and coincidence points of hybrid mappings, Arch. math. (Brno), 38, 201-208, (2002) · Zbl 1068.47073 [12] Sahab, S.A.; Khan, M.S.; Sessa, S., A result in best approximation theory, J. approx. theory, 55, 349-351, (1988) · Zbl 0676.41031 [13] Sessa, S., On a weak commutative condition of mappings in fixed point considerations, Publ. inst. math. (beograd) (N.S.), 32, 46, 149-153, (1982) · Zbl 0523.54030 [14] Shahzad, N., A result on best approximation, Tamkang J. math., Corrections, 30, 165-226, (1999) [15] Shahzad, N., On R-subcommuting maps and best approximations in Banach spaces, Tamkang J. math., 32, 51-53, (2001) · Zbl 0978.41020 [16] Shahzad, N., Invariant approximations and R-subweakly commuting maps, J. math. anal. appl., 257, 39-45, (2001) · Zbl 0989.47047 [17] Shahzad, N., Generalized I-nonexpansive maps and best approximations in Banach spaces, Demonstratio math., 37, 597-600, (2004) · Zbl 1095.41017 [18] Shahzad, N., Invariant approximations, generalized I-contractions, and R-subweakly commuting maps, Fixed point theory appl., 1, 79-86, (2005) · Zbl 1083.54540 [19] Singh, S.P., An application of fixed point theorem to approximation theory, J. approx. theory, 25, 89-90, (1979) · Zbl 0399.41032 [20] Subrahmanyam, P.V., An application of a fixed point theorem to best approximation, J. approx. theory, 20, 165-172, (1977) · Zbl 0349.41013
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