Abstract
We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces (not) satisfying weak L-P property and apply the concept to compute the exact number of extreme contractions between a particular pair of polygonal Banach spaces. We also study the optimality of our results on the newly introduced weak L-P property for a pair of Banach spaces, by considering appropriate examples.
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