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Problem statement: The object of this study is to obtain certain differential subordinations. Approach: Here we use known generalized differential operator given by Darus and Ibrahim and well known lemmas given by Miller and Mocanu. Results: We will pose several results on subordination theorems. Conclusion: Many other results can be obtained by using the operator defined.doi:10.3844/jmssp.2012.165.168 fatcat:autwm6rqlnhl7nbarzyammdsrm