Convergence to common fixed point for two asymptotically quasi-nonexpansive mappings in the intermediate sense in Banach spaces - Saluja Singh Gurucharan (Mathematica Moravica, 2015)
Suppose K is a nonempty closed convex subset of a real uniformly convex Banach space E. Let S; T : K → K be two asymptotically quasi-nonexpansive mappings in the intermediate sense such that F = F(S) ∩ F(T) = {x _ K : Sx = Tx = x} ≠ 0 ;. Suppose {xn} is generated iteratively by x1_K, xn+1 = (1 - ɑn)Tnxn + ɑnSnyn, yn = (1 - βn)xn + βnTnxn, n ɑ 1, where {ɑn} and {ɑn} are real sequences in [a; b] for some a; b _ (0; 1). If S and T satisfy condition (B) or either S or T is semi-compact, then the sequence fxng converges strongly to some q _ F and if E satisfying the Opial's condition, then the sequence {xn} converges weakly to some q _ F.