Abstract
Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.
Highlights
Let Y be a1realulinear space of dimensionlgreater than 1 and ‖.,...,.‖ : Y theifollowing conditions: a )1‖,..., ‖ = 0 if and1only if,..., are linearlyldependent vectors; b )1‖,..., ‖ is invariant1under permutations of,..., ; c ) ‖,..., ‖ = | |‖,..., ‖ for all R and,..., YY R satisfying d ) ‖ +,..., ‖ ≤ ‖,..., ‖+‖,..., ‖ for all,..., Y ‖.,...,.‖ is calledgan n-norm on Y and (Y,‖.,...,.‖) is calledfa linear n-normed spacek[1], In the1following,"wefneed the concept of n-Banach1space
In"1965, Browder [3] and Ghde [4] independently proved that every1nonexpansive self-mapping of a closedeconvex and "bounded subset of a uniformly convex Banach space has a fixed point
In [5],1It is shown that a technique of Mann is1fruitful in finding a fixed point on Banach space of monotone nonexpansive mapping
Summary
A sequence { } in n-normed space (Y,‖.,...,.‖) is said to be a converge to x X, if for all In"1965, Browder [3] and Ghde [4] independently proved that every1nonexpansive self-mapping of a closedeconvex and "bounded subset of a uniformly convex Banach space has a fixed point. In [5],1It is shown that a technique of Mann is1fruitful in finding a fixed point on Banach space of monotone nonexpansive mapping.
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