We enrich the known results about tripled fixed points and best proximity points. generalize notion of ordered pairs cyclic contraction maps we obtain sufficient conditions for existence uniqueness (or proximity) get a priori posteriori error estimates points, provided that underlying Banach space has modulus convexity power type in case obtained by sequences successive iterations. illustrate m...

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.