Abstract
In this article, we study the Agarwal iterative process for finding fixed points and best proximity points of relatively nonexpansive mappings. Using the Von Neumann sequence, we establish the convergence result in a Hilbert space framework. We present a new example of relatively nonexpansive mapping and prove that its Agarwal iterative process is more efficient than the Mann and Ishikawa iterative processes.
Highlights
Let E be a nonempty subset of a Banach space X
One of the celebrated result of Kirk [1] states that any self nonexpansive mapping of closed bounded convex subset E of a reflexive Banach space has a fixed point provided that E has normal structure. is result was independently proved in the same year by Browder [2] and Gohde [3] in uniformly convex Banach space
We present a new example of relatively nonexansive mapping and prove Journal of Mathematics that its Agarwal iterative process is more efficient than the Mann [29] and Ishikawa [31] iterative processes
Summary
Let E be a nonempty subset of a Banach space X. Suppose E be a nonempty bounded closed convex subset of a UCBS X, and assume that T be a self-map nonexpansive map of E. Suppose H and L are two nonempty bounded closed convex subsets of a UCBS X, and assume that T: H ∪ L ⟶ H ∪ L is such that
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