Abstract
Abstract The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Agarwal et al. (J. Nonlinear Convex. Anal. 8(1): 61-79, 2007), associated with nonexpansive and ϕ-hemicontractive mappings in a nonempty convex subset of an arbitrary Banach space.
Highlights
The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Agarwal et al
Theorem Let K be a nonempty closed and convex subset of an arbitrary Banach space X, let S : K → K be nonexpansive, and let T : K → K be a uniformly continuous φ-hemicontractive mapping such that S and T have the common fixed point
The known results for strongly pseudocontractive mappings are weakened by the φ-hemicontractive mappings
Summary
The purpose of this paper is to characterize the conditions for the convergence of the iterative scheme in the sense of Agarwal et al For a nonempty convex subset K of a normed space X, S : K → K and T : K → K , (a) the Mann iteration scheme [ ] is defined by the following sequence {xn}: Bnxn + ( – bn)Txn, = bnTxn + ( – bn)Tyn, n ≥ , (ARSn) where {bn}, {bn} are sequences in [ , ], is known as the Agarwal-O’Regan-Sahu [ ] iteration scheme; (d) the sequence {xn} defined by
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