In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space with a uniformly G$\hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(\ell_{p})$ spaces, $1 < p <\infty$ and consequently in sobolev spaces.
Ugwunnadi, G. (2016). Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings. International Journal of Nonlinear Analysis and Applications, 7(2), 93-108. doi: 10.22075/ijnaa.2016.479
MLA
Godwin Chidi Ugwunnadi. "Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings". International Journal of Nonlinear Analysis and Applications, 7, 2, 2016, 93-108. doi: 10.22075/ijnaa.2016.479
HARVARD
Ugwunnadi, G. (2016). 'Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings', International Journal of Nonlinear Analysis and Applications, 7(2), pp. 93-108. doi: 10.22075/ijnaa.2016.479
VANCOUVER
Ugwunnadi, G. Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings. International Journal of Nonlinear Analysis and Applications, 2016; 7(2): 93-108. doi: 10.22075/ijnaa.2016.479
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