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1. Introduction. In this paper, we shall be concerned with the solution of triple integral equations of the type Ji~ '[(1 +s)"M(s); /•] = 0 M ~1 [cot (ns/n)i4(s); r] = /(/•) (0 < r < a), (a < r < b), (b<r< oo), (1.1) where M ' is the inverse Mellin transform, n is a positive integer, and -1 < Re5 < 0. The use of these equations will be illustrated by their application to two well-known problems in the mathematical theory of elasticity and further applications will be reported later. We begin bydoi:10.1017/s0017089500001749 fatcat:tq53gy7anvcbdivbcufivstsvi