In this paper, we generalize the concept of well-posedness to a system of hemivariational inequalities in Banach space. By introducing several concepts of well-posedness for systems of hemivariational inequalities considered, we establish some metric characterizations of well-posedness and prove some equivalence results of strong (generalized) well-posedness between a system of hemivariational inequalities and its derived system of inclusion problems.

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In this paper, we generalized the notion of proximal contractions of the first and second kinds by using Geraghty's theorem and establish best proximity point theorems for proximal contractions. Our results improve and extend the recent results of Sadiq Basha and some others. MSC: 47H09; 47H10

In this paper we extend the notion of weakly C-contraction mappings to the case of non-self mappings and establish the best proximity point theorems for this class. Our results generalize the result due to Harjani et al. (Comput. Math. Appl. 61:790-796, 2011) and some other authors.