Common Fixed Points and Invariant Approximations for C-q-commuting Generalized nonexpansive mappings

Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and J. K. Kim [Bull. Korean Math. Soc. 44(2007) 537545], I. Beg, N. Shahzad and M. Iqbal [Approx. Theory Appl. 8(1992) 97-105], W. G. Dotson [J. London Math. Soc. 4(1972) 408-410; Proc. Amer. Math. Soc. 38(1973) 155-156.], M. D. Guay, K. L. Singh and J. H. M. Whitfield [Proc. Conference on nonlinear analysis (Ed. S. P. Singh and J. H. Bury) Marcel Dekker 80(1982) 179-189], L. Habiniak [J. Approx. Theory 56(1989) 241-244], N. Hussain and B. E. Rhoades [Fixed Point Theory Appl. Vol. 2006, Article ID 24543, 1-9], T. D. Narang and S. Chandok [Indian J. Math. 51(2009) 293-303; Ukrainian Math. J. 62 (2010) 1367-1376], N. Shahzad [Fixed point Theory Appl. 1(2005) 79-86] and of Y. Song [Comm. Math. Anal. 2(2007) 17-26].