scholarly journals New sufficient conditions for starlikeness of analytic functions involving a fractional differintegral operator

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
J. K. Prajapat ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Fractional Differintegral ◽  
Class Of Functions ◽  
Fractional Differintegral Operator

AbstractIn this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.

scholarly journals Convolution Properties of p-Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Priyabrat Gochhayat
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Fractional Differintegral ◽  
Convolution Properties ◽  
Class Of Functions ◽  
Fractional Differintegral Operator

Let 𝒜p denote the class of functions analytic in the open unit disc 𝕌 and given by the series f(z)=zp+∑n=p+1∞anzn. For f∈𝒜p, the transformation ℐp,δλ:𝒜p→𝒜p defined by ℐp,δλf(z)=zp+∑n=p+1∞((p+δ)/(n+δ))λanzn,  (δ+p∈ℂ∖ℤ0-,  λ∈ℂ;  z∈𝕌), has been recently studied as fractional differintegral operator by Mishra and Gochhayat (2010). In the present paper, we observed that ℐp,δλ can also be viewed as a generalization of the Srivastava-Attiya operator. Convolution preserving properties for a class of multivalent analytic functions involving an adaptation of the popular Srivastava-Attiya transform are investigated.

scholarly journals Certain Families of Multivalent Analytic Functions Associated with Iterations of the Owa-Srivastava Fractional Differintegral Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
A. K. Mishra ◽  
S. N. Kund
Keyword(s):  
Analytic Functions ◽  
Function Classes ◽  
Fractional Differintegral ◽  
Fractional Differintegral Operator

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.

scholarly journals A Generalized Class of Functions Defined by the q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2361
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
The Relationship ◽  
Class Of Functions

The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

scholarly journals Preserving properties of subordination and superordination of analytic functions associated with a fractional differintegral operator

2014 ◽  
Vol 45 (1) ◽  
pp. 63-75
Author(s):  
Jamal M. Shenan
Keyword(s):  
Analytic Functions ◽  
Type Result ◽  
Sandwich Type ◽  
Fractional Differintegral ◽  
Alpha Beta ◽  
Fractional Differintegral Operator

In this paper, we obtain some subordination and superordination-preserving results of analytic functions associated with the fractional differintegral operator $U_{0,z}^{\alpha ,\beta ,\gamma } $. Sandwich-type result involving this operator is also derived.

scholarly journals Some Inclusion Relations Associated with Generalized Fractional Differintegral Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Amit Soni ◽  
Shashi Kant
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Function Classes ◽  
Inclusion Relations ◽  
Fractional Differintegral ◽  
Fractional Differintegral Operator

A generalized fractional differintegral operator is used to define some new subclasses of analytic functions in the open unit disk . For each of these new function classes, several inclusion relationships are established.

Some new results on the subexponential class

1989 ◽  
Vol 26 (4) ◽  
pp. 892-897 ◽  
Author(s):  
Emily S. Murphree
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Subexponential Class ◽  
Class Of Functions

A distribution function F on (0,∞) belongs to the subexponential class if the ratio of 1 – F(2)(x) to 1 – F(x) converges to 2 as x →∞. A necessary condition for membership in is used to prove that a certain class of functions previously thought to be contained in has members outside of . Sufficient conditions on the tail of F are found which ensure F belongs to ; these conditions generalize previously published conditions.

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