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In the present paper a certain convolution operator of analytic functions is defined. Moreover, subordination- and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

Mathematics Subject Classification (2010): 30C45.

Keywords: Analytic function, convolution operator, differential subordination, differential superordination, sandwich theorem, best dominant and best subordinant.