Abstract

We prove strong convergence of an iterative scheme for approximation of fixed point of $\lambda$-strict pseudocontractive mapping in a uniformly smooth real Banach space (which is not necessarily uniformly convex). We apply our result to approximation of common fixed point of a finite family of strictly pseudocontractive mappings. Our result extends the results of Li and Yao [M. Li, Y. Yao, Strong convergence of an iterative algorithm for $\lambda$-strictly pseudocontractive mappings in Hilbert spaces, An. St. Univ. Ovidius Constanta 18 (2010), 219-228] and complements other new interesting results in the literature.

Keywords: Strong convergence; strictly pseudocontractive mappings; uniformly smooth Banach spaces; uniformly convex Banach spaces.

MSC: 47H06, 47H09, 47J05, 47J25

Pages:  79$-$91     

Volume  67 ,  Issue  2 ,  2015