Abstract
Iff is a self mapping on a closed convex subsetK of a separated quasicomplete locally convex linear topological spaceE such that (i)E is strictly convex, (ii)f (K) is contained in a compact subset ofK and (iii)f satisfies a contraction condition, then it is shown that for eachx∈K, the sequence of {U nλ (x)} ∞n =1 of iterates, whereU λ ∶K→K is defined byU λ (y)=λf(y)+(1-λ) y, y∈K, converges to a fixed point off.
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Tarafdar, E. On a fixed-point theorem on locally convex linear topological spaces. Monatshefte für Mathematik 82, 341–344 (1976). https://doi.org/10.1007/BF01540605
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DOI: https://doi.org/10.1007/BF01540605