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Subordination and Superordination for Multivalent Functions Associated with the Dziok-Srivastava Operator  [cached]
Cho NakEun,Kwon OhSang,Ali RosihanM,Ravichandran V
Journal of Inequalities and Applications , 2011,
Abstract: Subordination and superordination preserving properties for multivalent functions in the open unit disk associated with the Dziok-Srivastava operator are derived. Sandwich-type theorems for these multivalent functions are also obtained.
Subordination and superordination for multivalent functions defined by linear operators  [PDF]
S. Sivaprasad Kumar,Virendra Kumar,V. Ravichandran
Mathematics , 2011,
Abstract: In this paper, certain linear operators defined on $p$-valent analytic functions have been unified and for them some subordination and superordination results as well as the corresponding sandwich type results are obtained. A related integral transform is discussed and sufficient conditions for functions in different classes have been obtained.
Subordination and Superordination Results for a Class of Analytic Multivalent Functions  [PDF]
S. P. Goyal,Pranay Goswami,H. Silverman
International Journal of Mathematics and Mathematical Sciences , 2008, DOI: 10.1155/2008/561638
Abstract: We derive subordination and superordination results for a family of normalized analytic functions in the open unit disk defined by integral operators. We apply this to obtain sandwich results and generalizations of some known results.
Subordination and superordination properties for analytic functions involving Wright’s functions  [cached]
G. Murugusundaramoorthy,N. Magesh,R. K. Raina
Le Matematiche , 2011,
Abstract: In the present investigation, we obtain some subordination and superordination results for the Hadamard product of certain normalized analytic functions in the open unit disk involving the linear operator introduced in [J. Dziok and R. K. Raina, Demonstratio Math., 37 (3) (2004), 533–542]. Several consequences of the results are presented. It is also pointed out that one of the main results (Theorem 2.8 below) provides a corrected form of the proof stated in two recent known results.
Certain Families of Multivalent Analytic Functions Associated with Iterations of the Owa-Srivastava Fractional Differintegral Operator  [PDF]
A. K. Mishra,S. N. Kund
Journal of Complex Analysis , 2014, DOI: 10.1155/2014/915385
Abstract: By making use of a multivalent analogue of the Owa-Srivastava fractional differintegral operator and its iterations, certain new families of analytic functions are introduced. Several interesting properties of these function classes, such as convolution theorems, inclusion theorems, and class-preserving transforms, are studied. 1. Introduction Let denote the class of analytic functions in the open unit disk and let be the subclass of consisting of functions represented by the following Taylor-Maclaurin’s series: In a recent paper Patel and Mishra [1] studied several interesting mapping properties of the fractional differintegral operator: defined by where is given by (2). In the particular case and the fractional-differintegral operator was earlier introduced by Owa and Srivastava [2] (see also [3]) and this is popularly known as the Owa-Srivastava operator [4–6]. Moreover, for and , was investigated by Srivastava and Aouf [7] which was further extended to the range ,?? by Srivastava and Mishra [8]. The following are some of the interesting particular cases of : Furthermore The -iterates of the operator are defined as follows: and, for , Similarly, for , represented by (2), let the operator be defined by the following: and, for , Very recently Srivastava et al. [6] considered the composition of the operators and and introduced the following operator: That is, for , given by (2), we know that The transformation includes, among many, the following two previously studied interesting operators as particular cases. (i)For , , , the fractional derivative operator was recently introduced and investigated by Al-Oboudi and Al-Amoudi [9, 10], in the context of functions represented by conical domains.(ii)For , , , , is the S?l?gean operator [11], which is, in fact, the -iterates of the popular Alexander’s differential transform [12]. We next recall the definition of subordination. Suppose that and in is univalent in . We say that is subordinate to in if and . Considering the function , it is readily checked that satisfies the conditions of the Schwarz lemma and In a broader sense the function is said to be subordinate to the function ( need not be univalent in ), written as if condition (15) holds for some Schwarz function (see [12] for details). We also need the following definition of Hadamard product (or convolution). For the functions and in , given by the following Taylor-Maclaurin’s series their Hadamard product (or convolution) is defined by It is easy to see that . The study of iterations of entire and meromorphic functions, as the number of iterations
Some differential subordination and superordination properties of symmetric analytic functions involving Noor integral operator  [cached]
Ali Muhammad,Amjad Ullah Khattak
Le Matematiche , 2012,
Abstract: In this paper, we obtain some interesting properties of differential subordination and superordination for the classes of symmetric functions analytic in the unit disc, by applying Noor integral operator. We investigate several sandwich theorems on the basis of this theory.
Subordination and superordination for certain analytic functions containing fractional integral
Rabha W. Ibrahim,Maslina Darus,Shaher Momani
Surveys in Mathematics and its Applications , 2009,
Abstract: The purpose of the present article is to derive some subordination and superordination results for certain normalized analytic functions involving fractional integral operator. Moreover, this result is applied to find a relation between univalent solutions for fractional differential equation.
Subordination and Superordination on Schwarzian Derivatives
Ali RosihanM,Ravichandran V,Seenivasagan N
Journal of Inequalities and Applications , 2008,
Abstract: Let the functions be analytic and let be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function are obtained so that either or . As applications, sufficient conditions are determined relating the Schwarzian derivative to the starlikeness or convexity of .
Subordination and Superordination on Schwarzian Derivatives
Rosihan M. Ali,V. Ravichandran,N. Seenivasagan
Journal of Inequalities and Applications , 2009, DOI: 10.1155/2008/712328
Abstract: Let the functions q1 be analytic and let q2 be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function f are obtained so that either q1(z) ¢ ‰ ozf ¢ € 2(z)/f(z) ¢ ‰ oq2(z) or q1(z) ¢ ‰ o1+zf ¢ € 2 ¢ € 2(z)/f ¢ € 2(z) ¢ ‰ oq2(z). As applications, sufficient conditions are determined relating the Schwarzian derivative to the starlikeness or convexity of f.
Differential subordination for meromorphic multivalent quasi-convex functions
Rabha W. Ibrahim and M. Darus
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE , 2010,
Abstract: We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.
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