Abstract. Let $A$ be a non-empty approximately compact convex subset, $B$ be a non-empty closed convex subset and $C$ be a non-empty convex subset of a normed linear space $E$. Given a multifunction $T_1\colon A \longrightarrow2^C$ with open fibres, a Kakutani factorizable multifunction $T_2\colon C\longrightarrow2^B$ and a single valued function $g\colon A \longrightarrow A$, best proximity pair theorems furnishing the sufficient conditions for the existence of an element $x_\circ\in A$ such that $$ d(gx_{\circ }, T_2 T_1 x_{\circ }) = d(A, B) $$ are explored. As a consequence, a generalization of Ko and Tan's coincidence theorem is obtained.
AMS Subject Classification
(1991): 47H10, 54H25
Keyword(s):
Best proximity pairs,
Kakutani factorizable multifunctions,
Multifunctions with open fibres,
Proper map,
Quasi affine map
Received March 9, 2000. (Registered under 2793/2009.)
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