Geodesic
An analog of Gonchar's theorem for the $m$-point version of Leighton's conjecture
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 133-145

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Gonchar's theorem on the validity of Leighton's conjecture for arbitrary nondecreasing sequences of exponents of general $C$-fractions is extended to continued fractions of a more general form. 
@article{TM_2016_293_a8,
     author = {V. I. Buslaev},
     title = {An analog of {Gonchar's} theorem for the $m$-point version of {Leighton's} conjecture},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {133--145},
     publisher = {mathdoc},
     volume = {293},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_293_a8/}
}
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V. I. Buslaev. An analog of Gonchar's theorem for the $m$-point version of Leighton's conjecture. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 133-145. http://geodesic.mathdoc.fr/item/TM_2016_293_a8/