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Research ArticleOpen accessOn Applications of Differential Subordination and Differential OperatorM. Darus, R. W. IbrahimProblem 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. …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 1 Mar 2012 · 7,002 accessesView PDFCite
Research ArticleOpen accessOn a Univalent Class Involving Differential Subordinations with ApplicationsR. W. Ibrahim, M. DarusProblem statement: By means of the Hadamard product (or convolution), new class of analytic functions was formed. This class was motivated by many authors. Approach: By using the concept of the subordination and superordination, we define certain differential inequalities and first order differential subordinations. Results: As their applications, we obtain some sufficient conditions for univalence which generalize and refine some … …Journal of Mathematics and Statistics, Vol. 7, Issue 2 · 18 May 2011 · 7,532 accessesView PDFCite