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In the present paper we introduce a new q-generalization of Szász-Mirakjan operators and we investigate their approximation properties. By using a weighted modulus of smoothness, we give local and global estimations for the error of approximation.

Mathematics Subject Classification (2010): 41A36, 41A25.

Keywords: q-calculus, Szász-Mirakjan operator, Bohman-Korovkin type theorem, weighted space, weighted modulus of smoothness.