Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Naseer Shahzad, Aniefiok Udomene · Fixed Point Theory and Applications · 2006
Abstract Suppose "Equation missing" is a nonempty closed convex subset of a real Banach space "Equation missing". Let "Equation missing" be two asymptotically quasi-nonexpansive maps with sequences "Equation missing" such that "Equation missing" and "Equation missing", and "Equation missing". Suppose "Equation missing" is generated iteratively by "Equation missing" where "Equation missing" and "Equation missing" are real sequences in "Equation missing". It is proved that (a) "Equation missing" converges strongly to some "Equation missing" if and only if "Equation missing"; (b) if "Equation missing" is uniformly convex and if either "Equation missing" or "Equation missing" is compact, then "Equation missing" converges strongly to some "Equation missing". Furthermore, if "Equation missing" is uniformly convex, either "Equation missing" or "Equation missing" is compact and "Equation missing" is generated by "Equation missing", where "Equation missing", "Equation missing" are bounded, "Equation missing" are real sequences in "Equation missing" such that "Equation missing" and "Equation missing", "Equation missing" are summable; it is established that the sequence "Equation missing" (with error member terms) converges strongly to some "Equation missing".