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

Let $$[a_1(x),a_2(x),a_3(x),\cdots ]$$ be the continued fraction expansion of $$x\in (0,1)$$ . This paper is concerned with certain sets fractions non-decreasing partial quotients. As a main result, we obtain Hausdorff dimension set $$\begin{aligned} \left\{ x\in (0,1): a_1(x)\le a_2(x)\le \cdots ,\ \limsup \limits _{n\rightarrow \infty }\frac{\log a_n(x)}{\psi (n)}=1\right\} \end{aligned}$$ for any $$\psi :\mathbb {N}\rightarrow \mathbb {R}^+$$ satisfying (n)\rightarrow $$ as $$n\rightarrow