Abstract
The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature.
Highlights
Let T be a selfmap on a subset W of a Banach space U = (U, ||.||)
In 1922, Banach [1] proved that any self contraction map of a closed subset W of a Banach space has a unique fixed point
We present a new example of maps satisfying ( E)-condition, and prove that its under the consideration three-step iterative process is more efficient than the other well-known three-step iterative processes
Summary
Let T be a selfmap on a subset W of a Banach space U = (U, ||.||). T is called contraction map on W if for each pair of elements w, w0 ∈ W, there is some real constant α ∈ [0, 1), such that. If (1) holds at α = 1, T is called non-expansive. In 1922, Banach [1] proved that any self contraction map of a closed subset W of a Banach space has a unique fixed point. The Banach result [1] was extended by Caccioppoli [2] in complete metric spaces. In 1965, Browder [3] and Gohde [4] proved that any self non-expansive map of a convex bounded closed subset W of a uniformly convex Banach space U always admits a fixed point
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