Dimension of certain sets of regular and minus continued fractions with positive partial quotients

An estimate for the Hausdorff dimension of x\, ∈ \, R whose partial quotients of its regular continued fraction or minus continued fraction (MCF) are in E \, ⊆ \, N is given. This enables us to give a new proof for the Texan conjecture on [0,\,1/2] which is valid for both regular and MCF. Also we show that if E \, ⊆ \,N and ∑e \, ∈ \, E \,1/e \, = \, ∞ , then the Hausdorff dimension of E is at least 1/2 .