Abstract
The purpose of this paper is to investigate the strong convergence problem of a modified mixed Ishikawa iterative sequence with errors for approximating the fixed points of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-pseudo-contractive-type mapping in an arbitrary real Banach space. The results here improve and extend the corresponding results reported by some other authors recently.
Highlights
Introduction and PreliminariesIt is well known that fixed point theory has emerged as an important tool in studying a wide class of nonlinear elliptic systems and nonlinear parabolic systems, obstacle, unilateral, and equilibrium problems, optimization problems, theoretical mechanics, and control theory, which arise in several branches of pure and applied nonlinear sciences in a unified and general framework
The purpose of this paper is to investigate the strong convergence problem of a modified mixed Ishikawa iterative sequence with errors for approximating the fixed points of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-pseudo-contractive-type mapping in an arbitrary real Banach space
The modified Ishikawa and Mann iterative sequences with errors were studied by Zeng. He [4] proved the strong convergence of the modified Ishikawa iterative sequence with errors for the uniformly L-Lipschitzian asymptotically pseudocontractive mapping in an arbitrary real Banach space with the bounded range of T
Summary
Introduction and PreliminariesIt is well known that fixed point theory has emerged as an important tool in studying a wide class of nonlinear elliptic systems and nonlinear parabolic systems, obstacle, unilateral, and equilibrium problems, optimization problems, theoretical mechanics, and control theory, which arise in several branches of pure and applied nonlinear sciences in a unified and general framework. (1) The mapping T is said to be asymptotically nonexpansive, if there exists a number sequence {kn} ⊂ [1, ∞) with limn → ∞kn = 1, such that Tnx − Tny ≤ kn x − y , ∀x, y ∈ G, n ≥ 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
