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If a weakly compact convex set K in a real Banach space X is strongly exposed by a dense set of functionals in X', it is proved that the functionals which expose K form a residual set in A". If v. & -* X is a measure, it follows that the set of exposing functionals of its range is a residual Gs in A". This, in turn, is found to be equivalent to a theorem of B. Walsh on the residuality of functi...

We show that for every positive integer d, every downwards closed subtree T of d without terminal nodes and every finite weakly embedded subtree A of T there is a finite list of equivalence relations on Em(T ) with the property that for every other equivalence relation E on Em(T ) there is a strongly embedded subtree S ⊆ T of height ω, such that E Em(S) is equal to one of the equivalence relati...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...