Journal of Complex Analysis
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The latest articles from Hindawi Publishing Corporation
© 2016 , Hindawi Publishing Corporation . All rights reserved.

Dirichlet Problem for Complex Poisson Equation in a Half Hexagon Domain
Wed, 10 Feb 2016 11:47:26 +0000
http://www.hindawi.com/journals/jca/2016/8097095/
The parquetingreflection method is applied to a nonregular domain and the harmonic Green function for the half hexagon is constructed. The related Dirichlet problem for the Poisson equation is solved explicitly.
Bibinur Shupeyeva
Copyright © 2016 Bibinur Shupeyeva. All rights reserved.

Sharp Estimates for Green’s Functions of ConeType Planar Domains
Wed, 10 Feb 2016 07:57:14 +0000
http://www.hindawi.com/journals/jca/2016/7208285/
We establish sharp estimates for Green’s functions of conetype planar domains. Our work generalizes all estimates given by Zhao in 1988 and Selmi in 2000. Our principal idea is to use conformal mappings.
Mohamed Amine Ben Boubaker and Mohamed Selmi
Copyright © 2016 Mohamed Amine Ben Boubaker and Mohamed Selmi. All rights reserved.

An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics
Thu, 05 Nov 2015 14:33:33 +0000
http://www.hindawi.com/journals/jca/2015/259167/
We present a new fourth order method for finding simple roots of a nonlinear equation . In terms of computational cost, per iteration the method uses one evaluation of the function and two evaluations of its first derivative. Therefore, the method has optimal order with efficiency index 1.587 which is better than efficiency index 1.414 of Newton method and the same with Jarratt method and Kingâ€™s family. Numerical examples are given to support that the method thus obtained is competitive with other similar robust methods. The conjugacy maps and extraneous fixed points of the presented method and other existing fourth order methods are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane.
Rajni Sharma and Ashu Bahl
Copyright © 2015 Rajni Sharma and Ashu Bahl. All rights reserved.

Good Linear Operators and Meromorphic Solutions of Functional Equations
Thu, 14 May 2015 14:12:16 +0000
http://www.hindawi.com/journals/jca/2015/960204/
Nevanlinna theory provides us with many tools applicable to the study of value distribution of meromorphic solutions of differential equations. Analogues of some of these tools have been recently developed for difference, difference, and ultradiscrete equations. In many cases, the methodologies used in the study of meromorphic solutions of differential, difference, and difference equations are largely similar. The purpose of this paper is to collect some of these tools in a common toolbox for the study of general classes of functional equations by introducing notion of a good linear operator, which satisfies certain regularity conditions in terms of value distribution theory. As an example case, we apply our methods to study the growth of meromorphic solutions of the functional equation , where is a linear polynomial in and , where is good linear operator, is a polynomial in with degree deg , both with small meromorphic coefficients, and is a meromorphic function.
Nan Li, Risto Korhonen, and Lianzhong Yang
Copyright © 2015 Nan Li et al. All rights reserved.

On Certain Subclasses of Analytic Functions Involving CarlsonShaffer Operator and Related to Lemniscate of Bernoulli
Tue, 16 Dec 2014 06:35:11 +0000
http://www.hindawi.com/journals/jca/2014/295703/
The object of the present investigation is to solve the FeketeSzegö problem and determine the sharp upper bound to the second Hankel determinant for a new class of analytic functions involving the CarlsonShaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.
Jagannath Patel and Ashok Kumar Sahoo
Copyright © 2014 Jagannath Patel and Ashok Kumar Sahoo. All rights reserved.

Coefficient Estimates for a New Subclass of Analytic and BiUnivalent Functions Defined by Hadamard Product
Mon, 10 Nov 2014 12:03:00 +0000
http://www.hindawi.com/journals/jca/2014/302019/
We introduce and investigate a new general subclass of analytic and biunivalent functions in the open unit disk . For functions belonging to this class, we obtain estimates on the first two TaylorMaclaurin coefficients and .
Serap Bulut
Copyright © 2014 Serap Bulut. All rights reserved.

Certain Families of Multivalent Analytic Functions Associated with Iterations of the OwaSrivastava Fractional Differintegral Operator
Tue, 14 Oct 2014 11:26:39 +0000
http://www.hindawi.com/journals/jca/2014/915385/
By making use of a multivalent analogue of the
OwaSrivastava 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
classpreserving transforms, are studied.
A. K. Mishra and S. N. Kund
Copyright © 2014 A. K. Mishra and S. N. Kund. All rights reserved.

Certain Admissible Classes of Multivalent Functions
Tue, 16 Sep 2014 00:00:00 +0000
http://www.hindawi.com/journals/jca/2014/936748/
We investigate some applications of the differential subordination and the differential superordination of certain admissible classes of multivalent functions in the open unit disk . Several differential sandwichtype results are also obtained.
M. K. Aouf, H. M. Srivastava, and T. M. Seoudy
Copyright © 2014 M. K. Aouf et al. All rights reserved.

Growth Analysis of Composite Entire Functions Related to Slowly Changing Functions Oriented Relative Order and Relative Type
Mon, 08 Sep 2014 05:33:53 +0000
http://www.hindawi.com/journals/jca/2014/503719/
Some results on comparative growth properties of maximum terms and maximum moduli of composite entire functions on the basis of relative order and relative type are proved in this paper.
Sanjib Kumar Datta, Tanmay Biswas, and Sarmila Bhattacharyya
Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved.

Summation Formulas Obtained by Means of the Generalized Chain Rule for Fractional Derivatives
Thu, 28 Aug 2014 11:49:00 +0000
http://www.hindawi.com/journals/jca/2014/820951/
In 1970, several interesting new summation formulas were obtained by using a generalized chain rule for fractional derivatives. The main object of
this paper is to obtain a presumably new general formula. Many special cases involving special functions of mathematical physics such as the generalized hypergeometric functions, the Appell function, and the Lauricella functions of several variables are given.
S. Gaboury and R. Tremblay
Copyright © 2014 S. Gaboury and R. Tremblay. All rights reserved.

A New Class of Meromorphic Functions Involving the Polylogarithm Function
Mon, 11 Aug 2014 08:11:11 +0000
http://www.hindawi.com/journals/jca/2014/864805/
We introduce a new operator associated with polylogarithm function. By making use of the new operator, we define a certain new class of meromorphic functions and discussed some important properties of it.
Khadeejah Rasheed Alhindi and Maslina Darus
Copyright © 2014 Khadeejah Rasheed Alhindi and Maslina Darus. All rights reserved.

Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques
Tue, 01 Jul 2014 09:31:11 +0000
http://www.hindawi.com/journals/jca/2014/473069/
Let , denote the class of all normalized analytic functions in the unit disc such that for some with , and . Let , , denote the Pascu class of convex functions given by the analytic condition which unifies the classes of starlike and convex functions. The aim of this paper is to find conditions on so that the integral transform of the form
carry functions from into . As for the applications, for specific values of , it is found that several known integral operators carry functions from into . The results for a more generalized operator related to are also given.
Satwanti Devi and A. Swaminathan
Copyright © 2014 Satwanti Devi and A. Swaminathan. All rights reserved.

Weakly Weighted Sharing and Uniqueness of Meromorphic Functions
Thu, 22 May 2014 08:26:56 +0000
http://www.hindawi.com/journals/jca/2014/378958/
With the aid of the notion of weakly weighted sharing, we study the uniqueness of meromorphic
functions sharing four pairs of small functions. Our results improve and generalize some results
given by Czubiak and Gundersen, Li and Yang, and other authors.
Thamir Alzahary
Copyright © 2014 Thamir Alzahary. All rights reserved.

Coefficient Estimate of Biunivalent Functions of Complex Order Associated with the Hohlov Operator
Thu, 10 Apr 2014 09:35:38 +0000
http://www.hindawi.com/journals/jca/2014/693908/
We introduce and investigate a new subclass of the function class of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the TaylorMaclaurin coefficients and for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.
Z. Peng, G. Murugusundaramoorthy, and T. Janani
Copyright © 2014 Z. Peng et al. All rights reserved.

Generalized Growth of Special Monogenic Functions
Tue, 01 Apr 2014 07:42:00 +0000
http://www.hindawi.com/journals/jca/2014/510232/
We study the generalized growth of special monogenic functions. The characterizations of generalized order, generalized lower order, generalized type, and generalized lower type of special monogenic functions have been obtained in terms of their Taylor’s series coefficients.
Susheel Kumar
Copyright © 2014 Susheel Kumar. All rights reserved.

FeketeSzegö Inequalities for Starlike Functions with respect to Symmetric Points of Complex Order
Wed, 19 Mar 2014 09:02:54 +0000
http://www.hindawi.com/journals/jca/2014/131475/
Sharp upper bounds of for the function belonging to certain subclass of starlike functions with respect to symmetric points of complex order are obtained. Also, applications of our results to certain functions defined through convolution with a normalized analytic function are given. In particular, FeketeSzegö inequalities for certain classes of functions defined through fractional derivatives are obtained.
M. K. Aouf, R. M. ElAshwah, and S. M. ElDeeb
Copyright © 2014 M. K. Aouf et al. All rights reserved.

Coefficients of Meromorphic BiBazilevic Functions
Sun, 09 Mar 2014 08:03:26 +0000
http://www.hindawi.com/journals/jca/2014/263917/
A function is said to be biBazilevic in a given domain if both the function and its inverse map are Bazilevic there. Applying the Faber polynomial expansions to the meromorphic Bazilevic functions, we obtain the general coefficient bounds for biBazilevic functions. We also demonstrate the unpredictability of the behavior of early coefficients of biBazilevic functions.
Jay M. Jahangiri and Samaneh G. Hamidi
Copyright © 2014 Jay M. Jahangiri and Samaneh G. Hamidi. All rights reserved.

Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation
Tue, 25 Feb 2014 12:11:17 +0000
http://www.hindawi.com/journals/jca/2014/187482/
The main object of the present paper is to investigate several interesting subordination properties and a sharp inclusion relationship for certain subclass of multivalent analytic functions, which are defined here by the generalized multiplier transformation. Relevant connections of the results which are presented in this paper with various known results are also considered.
M. P. Jeyaraman and T. K. Suresh
Copyright © 2014 M. P. Jeyaraman and T. K. Suresh. All rights reserved.

An Application of a Poisson Distribution Series on Certain Analytic Functions
Tue, 18 Feb 2014 07:06:26 +0000
http://www.hindawi.com/journals/jca/2014/984135/
The purpose of the present paper is to introduce a Poisson distribution series and obtain necessary and sufficient conditions for this
series belonging to the classes and . We also consider
an integral operator related to this series.
Saurabh Porwal
Copyright © 2014 Saurabh Porwal. All rights reserved.

The Symmetric Versions of Rouché’s Theorem via Calculus
Tue, 04 Feb 2014 14:16:01 +0000
http://www.hindawi.com/journals/jca/2014/260953/
Let be a pair of holomorphic functions. In this expositional paper we apply the calculus to prove the symmetric version “ on ” as well as the homotopic version of Rouché's theorem for arbitrary planar compacta . Using Eilenberg's representation theorem we also give a converse to the homotopic version. Then we derive two analogs of Rouché's theorem for continuousholomorphic pairs (a symmetric and a nonsymmetric one). One of the rarely presented properties of the nonsymmetric version is that in the fundamental boundary hypothesis, , equality is allowed.
Raymond Mortini and Rudolf Rupp
Copyright © 2014 Raymond Mortini and Rudolf Rupp. All rights reserved.

On Angular Limits of Normal Meromorphic Functions: A Geometric Aspect
Mon, 20 Jan 2014 17:23:00 +0000
http://www.hindawi.com/journals/jca/2014/216398/
We will prove the assertions which give necessary and sufficient conditions for a normal meromorphic function on the open unit disk to have an angular limit. The results obtained show that the conditions from the classical Lindelöf theorem, as well as the theorems of Lehto and Virtanen and Bagemihl and Seidel, concerning angular limit values of meromorphic functions, can be weakened.
Zarko Pavicevic
Copyright © 2014 Zarko Pavicevic. All rights reserved.

Inclusion and Neighborhood Properties for Certain Classes of Multivalently Analytic Functions
Sun, 10 Nov 2013 10:12:16 +0000
http://www.hindawi.com/journals/jca/2013/754598/
We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the classes introduced here.
Serap Bulut
Copyright © 2013 Serap Bulut. All rights reserved.

Coefficient Estimate Problem for a New Subclass of Biunivalent Functions
Mon, 28 Oct 2013 14:25:44 +0000
http://www.hindawi.com/journals/jca/2013/474231/
We introduce a unified subclass of the function class of
biunivalent functions defined in the open unit disc. Furthermore, we find estimates on
the coefficients and for functions in this subclass. In addition, many relevant
connections with known or new results are pointed out.
N. Magesh, T. Rosy, and S. Varma
Copyright © 2013 N. Magesh et al. All rights reserved.

Subclass of Multivalent Harmonic Functions Defi…ned by Wright Generalized Hypergeometric Functions
Thu, 24 Oct 2013 09:25:40 +0000
http://www.hindawi.com/journals/jca/2013/397428/
We introduce a new class of multivalent harmonic functions defi…ned by Wright generalized hypergeometric function. Coefficient estimates, extreme points, distortion bounds, and convex combination for functions belonging to this class are obtained.
M. K. Aouf, A. O. Moustafa, and E. A. Adwan
Copyright © 2013 M. K. Aouf et al. All rights reserved.

Unique Range Set for Meromorphic Functions with Deficient Values
Sun, 20 Oct 2013 15:24:37 +0000
http://www.hindawi.com/journals/jca/2013/243606/
We employ the idea of weighted sharing of sets to find a unique range set for meromorphic functions with deficient values. Our result improves, generalises, and extends the result of Lahiri. Examples are exhibited that a condition in one of our results is the best possible one.
Abhijit Banerjee and Sujoy Majumder
Copyright © 2013 Abhijit Banerjee and Sujoy Majumder. All rights reserved.

Arc Length Inequality for a Certain Class of Analytic Functions Related to Conic Regions
Tue, 27 Aug 2013 14:12:11 +0000
http://www.hindawi.com/journals/jca/2013/407596/
In our present investigation, we
introduce a subclass of analytic function associated with conic regions
which is a form of generalized closetoconvexity. The arclength inequality
for a class of analytic function is well known. We derive this inequality
for the newly defined class and also study some of its interesting
consequences.
Wasim UlHaq, Muhammad Arif, and Asfandyar Khan
Copyright © 2013 Wasim UlHaq et al. All rights reserved.

Subclasses of Starlike Functions Associated with Fractional Calculus Operators
Sun, 28 Apr 2013 10:26:25 +0000
http://www.hindawi.com/journals/jca/2013/572718/
Making use of fractional calculus operators, we introduce a new subclass of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in . Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in .
G. Murugusundaramoorthy, C. Selvaraj, and O. S. Babu
Copyright © 2013 G. Murugusundaramoorthy et al. All rights reserved.

Subclasses of Harmonic Mappings Defined by Convolution
Mon, 08 Apr 2013 18:38:25 +0000
http://www.hindawi.com/journals/jca/2013/403624/
Two new subclasses of harmonic univalent functions defined by using convolution and integral convolution are introduced. These subclasses generate several known and new subclasses of harmonic univalent functions as special cases and provide a unified treatment in the study of these classes. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are also determined.
Santosh B. Joshi and Girish D. Shelake
Copyright © 2013 Santosh B. Joshi and Girish D. Shelake. All rights reserved.

Certain Subclasses of Valent Meromorphic
Functions Associated with a New Operator
Wed, 03 Apr 2013 14:15:59 +0000
http://www.hindawi.com/journals/jca/2013/851318/
We introduce two classes of valent meromorphic functions associated
with a new operator and derive several interesting results for these classes.
A. O. Mostafa, M. K. Aouf, A. Shamandy, and E. A. Adwan
Copyright © 2013 A. O. Mostafa et al. All rights reserved.

On the Regularity of Weak Contact Harmonic Maps
Mon, 25 Mar 2013 11:02:14 +0000
http://www.hindawi.com/journals/jca/2013/197410/
We prove Caccioppoli type estimates and consequently establish local Hölder continuity
for a class of weak contact harmonic maps from the
Heisenberg group into the sphere .
Sorin Dragomir and Robert Petit
Copyright © 2013 Sorin Dragomir and Robert Petit. All rights reserved.