Research ArticleOpen accessIn the keywordsOn 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
Research ArticleOpen accessIn the keywordsGeneralization of Differential OperatorMaslina Darus, Rabha W. IbrahimThe main objective of this study was to generalize a differential operator. The generalized differential operator reduced to many known operators studied by various authors. New classes containing this generalized operator were studied and characterization of these classes was obtained. Further, subordination and superordination results involving this operator were studied and obtained the sandwich theorem. …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 6,945 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn 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