ON COMMON FIXED POINTS OF A NEW ITERATION FOR TWO NONSELF ASYMPTOTICALLY QUASI-NONEXPANSIVETYPE-MAPPINGS IN BANACH SPACES

Abstract

Suppose that $K$ is a nonempty closed convex subset of a real Banach space E which is also a nonexpansive retract of E. Let $T, S: K \rightarrow E$ be two nonself asymptotically quasi-nonexpansive-type mappings of $E$ with $F = F (T)\cupF (S) := {x 2 K : Tx = x = Sx} \neq \emptyset$. Suppose ${x_n}$ is generated iteratively by $x_1 \in K,$
$x_{n+1} = P((1-a_n)x_n + a_n S(PS)^{n-1}((1-\beta_n)y_n+\beta_n S(PS)^{n-1}y_n))$
$y_n =P((1-b_n)x_n + a_n S(PS)^{n-1}((1-\gamma_n)y_n+\gamma_n S(PS)^{n-1}y_n))   n \geq 1,$
where  {a_n} , {b_n} , {\beta_n} , {\gamma_n} are appropriate sequences in [0, 1] . In this paper, we study the strongly converges to a common fixed point of the a new iterative scheme for two nonself asymptotically quasinonexpansivetype mappings in Banach spaces. The results obtained in this paper extend and improve the recent ones announced by Tan and Xu [16], Shahzad [12], Thianwan [15], Kiziltunc et al. [17] and many others.