We consider the problem of best proximity point in locally convex spaces endowed with a weakly convex digraph. For that, we introduce the notions of nonself G-contraction and G-nonexpansive mappings, and we show that for each seminorm, we have a best proximity point. In addition, we conclude our work with a result showing the existence of best proximity point for every seminorm.

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The main goal of this paper is to give some perturbation results and some relations between the essential pseudospectra of the sum of two multivalued linear operator and the essential pseudospectra of each of these multivalued linear operator. 2010 Mathematics Subject Classification: 47A06.

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