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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
Research ArticleOpen accessSome Properties of Certain Subclass of Meromorphically Multivalent Functions Defined By Linear OperatorF. Ghanim, M. DarusProblem statement: By means of the Hadamard product (or convolution), a linear operator was introduced. This operator was motivated by many authors namely Srivastava, Swaminathan, Owa and many others. The operator was indeed needed to create new ideas in the area of geometric function theory. Approach: The linear operator of meromorphic p-valent functions was proposed and defined. The preliminary concept … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,342 accessesView PDFCite
Research ArticleOpen accessSome Subordination Results Associated With Certain Subclass of Analytic Meromorphic FunctionsF. Ghanim, M. DarusFor functions belonging to each of the subclasses S*w (β) and C*w (β) of normalized analytic functions in the open unit disk D, which are investigated in this paper when 0≤β<1, the authors derive several subordination results involving the Hadamard product (or convolution) of the associated functions. A number of interesting consequences of some of these subordination results are also … …Journal of Mathematics and Statistics, Vol. 4, Issue 2 · 30 Jun 2008 · 6,879 accessesView PDFCite
Research ArticleOpen accessAn Operator Defined by Convolution Involving the Polylogarithms FunctionsK. Al Shaqsi, M. DarusWe define an operator on the class A of analytic functions in the unit disk U = {z :|z | < 1} involving the polylogarithms functions and introduce certain new subclasses of A using this operator. Some inclusion results, covering theorem, coefficients inequalities, and several other interesting properties of these classes are obtained. …Journal of Mathematics and Statistics, Vol. 4, Issue 1 · 31 Mar 2008 · 7,450 accessesView PDFCite