this paper is concerned with the best proximity pair problem in hilbert spaces. given two subsets $a$ and $b$ of a hilbert space $h$ and the set-valued maps $f:a o 2^ b$ and $g:a_0 o 2^{a_0}$, where $a_0={xin a: |x-y|=d(a,b)~~~mbox{for some}~~~ yin b}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in a$ such that $$d(g(x_0),f(x_0))=d(a,b).$$

In the present paper, we study existence of best proximity pair in ultrametric spaces. We show, under suitable assumptions, that proximinal $$(A,B)$$ has a pair. As consequence generalize well known approximation result and derive some fixed point theorems. Moreover, provide examples to illustrate obtained results.

The purpose of this article is to first introduce the notion of tripled best proximity point and cyclic contraction pair. We also establish the existence and convergence theorems of tripled best proximity points in metric spaces. Moreover, we apply our results to setting of uniformly convex Banach space. Finally, we obtain some results on the existence and convergence of tripled fixed point in ...

In this presentation, we discuss an intuitive model of the kinematics and dynamics of spatial compliant contact. The kinematic model gives a relation between the relative velocity of two rigid bodies and the velocities of two points on their surfaces that have smallest distance. The dynamic model uses a 6D spatial spring element to model the elastic forces between the bodies resulting from the ...