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In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.doi:10.2478/v10062-008-0011-5 fatcat:ccbbh3mwlzgkjkxn4qnpzpe2cu