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In this note, we will use a compactness type condition in connection with the weak topology to prove the existence of weakly continuous solutions for a functional integral equation of Volterra-Stieltjes type in nonreflexive Banach spaces. A special case will be considered. AMS Subject Classification: 35D30, 26A42, 47H10, 58C30, 28-XX

ON THE VOLTERRA-STIELTJES INTEGRAL EQUATION AND AXIOMATIC MEASURES OF WEAK NONCOMPACTNESS