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We define an alternate convexically nonexpansive map T on a bounded, closed, convex subset C of a Banach space X and prove that if X is a strictly convex Banach space and C is a nonempty weakly compact convex subset of X, then every alternate convexically nonexpansive map T : CC has a fixed point. As its application, we give an existence result for the solution of an integral equation.

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. P., Porosity and unique completion in strictly convex spaces, Math. Z. 267 ( 1-2 ) ( 2011 ), 173 - 184 . [17] Naszódi , M. and Visy

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