Convolution properties for certain subclass of analytic functions

2013 ◽  
Author(s):  
Norlyda Mohamed ◽  
Daud Mohamad ◽  
Shaharuddin Cik Soh
Keyword(s):  
Analytic Functions ◽  
Convolution Properties

New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

2019 ◽  
Vol 26 (3) ◽  
pp. 449-458
Author(s):  
Khalida Inayat Noor ◽  
Rashid Murtaza ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Convolution Properties ◽  
Appl Math ◽  
Inclusion Results

Abstract In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in {|z|<1} , by using the hypergeometric function and the Owa–Srivastava operator {\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

scholarly journals Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Sumbal Farman ◽  
S. M. Jawwad Riaz ◽  
Shabieh Farwa
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Janowski Functions ◽  
Convolution Properties ◽  
Inclusion Results

In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.

scholarly journals Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Convolution Properties

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

scholarly journals Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 105
Author(s):  
Abdel Moneim Y. Lashin ◽  
Badriah Maeed Algethami ◽  
Abeer O. Badghaish
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Inclusion Properties ◽  
Convolution Properties

In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods.

ON CERTAIN SUBCLASS OF p-VALENT NON-BAZILEVIC FUNCTIONS DEFINED BY THE DZIOK–SRIVASTAVA OPERATOR

2013 ◽  
Vol 06 (03) ◽  
pp. 1350032
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Bazilevic Functions

By making use of the principle of subordination and Dziok–Srivastava operator, we introduce a certain subclass of p-valent non-Bazilevic analytic functions. Such results as subordination and superordination properties, convolution properties, distortion theorems and inequality properties, are proved.

scholarly journals Convolution properties of a class of bounded analytic functions

1992 ◽  
Vol 45 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Zou Zhongzhu ◽  
Shigeyoshi Owa
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Class A ◽  
Convolution Properties ◽  
Class Of Functions

Let A be the class of functions f(z) which are analytic in the unit disk U with f(0) = f′(0) - 1 = 0. A subclass S(λ, M) (λ > 0, M > 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functions f(z) belonging to the class S(λ, M). Also a certain integral operator J for f(z) in the class A is considered.

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