Dimensions of certain sets of continued fractions with non-decreasing partial quotients

Let [a(1)(x), a(2)(x), a(3)( x), . . .] be the continued fraction expansion of x is an element of (0, 1). This paper is concerned with certain sets of continued fractions with non-decreasing partial quotients. As a main result, we obtain the Hausdorff dimension of the set {x is an element of(0, 1) : a(1)(x) <= a(2)(x) <= . . ., lim sup n -> infinity log a(n)(x)/psi(n) = 1}} for any psi : N -> R+ satisfying psi(n) -> infinity as n -> infinity.