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Let  T  be an expanding Markov map with a repeller  E  defined on. This paper concerns the Hausdorff dimension of the setsandwhereis a sequence of Lipschitz functions with a uniform Lipschitz constant,,  f  is a positive continuous function on,is the sumand  ψ  is a positive function defined on. The results can be applied to cookie-cutter dynamical systems and continued fraction dynamical systems, etc.

Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps