A further generalization of midpoint convexity of multimaps towards common fixed point theorems and applications

Irene Benedetti, Anna Martellotti

DOI: http://dx.doi.org/10.12775/TMNA.2015.039


We furtherly generalize midpoint convexity for multivalued maps and derive Fixed Point Theorems and Common Fixed Point Theorems without requiring strong compactness. As an application we obtain some Best Approximation results, and minimax and variational inequalities.


Common fixed points, midpoint convexity, commuting families of multimaps, best approximations, variational inequalities

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