in 2004, rodr'{i}guez-lallena and '{u}beda-flores have introduced a class of bivariate copulas which generalizes some known families such as the farlie-gumbel-morgenstern distributions. in 2006, dolati and '{u}beda-flores presented multivariate generalizations of this class. then in 2011, kim et al. generalized rodr'{i}guez-lallena and '{u}beda-flores' study to any...

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.