Journal of Complex Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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 Taylor-Maclaurin 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. Fekete-Szegö 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, Fekete-Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained. M. K. Aouf, R. M. El-Ashwah, and S. M. El-Deeb Copyright © 2014 M. K. Aouf et al. All rights reserved. Coefficients of Meromorphic Bi-Bazilevic Functions Sun, 09 Mar 2014 08:03:26 +0000 http://www.hindawi.com/journals/jca/2014/263917/ A function is said to be bi-Bazilevic 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 bi-Bazilevic functions. We also demonstrate the unpredictability of the behavior of early coefficients of bi-Bazilevic 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 continuous-holomorphic pairs (a symmetric and a nonsymmetric one). One of the rarely presented properties of the non-symmetric 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 close-to-convexity. The arc-length 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 Ul-Haq, Muhammad Arif, and Asfandyar Khan Copyright © 2013 Wasim Ul-Haq 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. Perturbations of Polynomials with Operator Coefficients Sun, 24 Mar 2013 08:42:35 +0000 http://www.hindawi.com/journals/jca/2013/801382/ We consider polynomials whose coefficients are operators belonging to the Schatten-von Neumann ideals of compact operators in a Hilbert space. Bounds for the spectra of perturbed pencils are established. Applications to differential and difference equations are also discussed. Michael Gil' Copyright © 2013 Michael Gil'. All rights reserved. On Certain New Subclass of Meromorphic Close-to-Convex Functions Mon, 11 Mar 2013 15:37:15 +0000 http://www.hindawi.com/journals/jca/2013/704784/ We introduce a certain new subclass of meromorphic close-to-convex functions. Such results as inclusion relationship, coefficient inequalities, distortion, and growth theorems for this class of functions are derived. Jing-Ping Yi, Zhi-Gang Wang, and Ming-Hua Zeng Copyright © 2013 Jing-Ping Yi et al. All rights reserved. Inequalities for Discrete Möbius Groups in Infinite Dimension Mon, 11 Mar 2013 12:59:24 +0000 http://www.hindawi.com/journals/jca/2013/515109/ We establish some inequalities for discrete Möbius groups in infinite dimension, which are generalizations of the corresponding results of Coa, 1996 and Gehring and Martin, 1991 in finite dimension. Xi Fu Copyright © 2013 Xi Fu. All rights reserved. Some New Explicit Values of Quotients of Theta-Function and Applications to Ramanujan's Continued Fractions Thu, 07 Mar 2013 15:12:33 +0000 http://www.hindawi.com/journals/jca/2013/538592/ We find some new explicit values of the parameter for positive real numbers and involving Ramanujan's theta-function and give some applications of these new values for the explicit evaluations of Ramanujan's continued fractions. In the process, we also establish two new identities for by using modular equations. Nipen Saikia Copyright © 2013 Nipen Saikia. All rights reserved. The Method of Fischer-Riesz Equations for Elliptic Boundary Value Problems Tue, 19 Feb 2013 11:18:13 +0000 http://www.hindawi.com/journals/jca/2013/486934/ We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first-order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well-elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem. A. Alsaedy and N. Tarkhanov Copyright © 2013 A. Alsaedy and N. Tarkhanov. All rights reserved. Convolution Properties of -Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator Thu, 07 Feb 2013 13:29:51 +0000 http://www.hindawi.com/journals/jca/2013/676027/ Let denote the class of functions analytic in the open unit disc and given by the series . For , the transformation defined by , has been recently studied as fractional differintegral operator by Mishra and Gochhayat (2010). In the present paper, we observed that 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. Priyabrat Gochhayat Copyright © 2013 Priyabrat Gochhayat. All rights reserved. New Subclasses of Analytic Functions with Respect to Symmetric and Conjugate Points Mon, 04 Feb 2013 10:17:32 +0000 http://www.hindawi.com/journals/jca/2013/578036/ We introduce new subclasses of close-to-convex and quasiconvex functions with respect to symmetric and conjugate points. The coefficient estimates for functions belonging to these classes are obtained. Huo Tang and Guan-Tie Deng Copyright © 2013 Huo Tang and Guan-Tie Deng. All rights reserved. Some Properties of Solutions of Second-Order Linear Differential Equations Wed, 30 Jan 2013 16:57:35 +0000 http://www.hindawi.com/journals/jca/2013/253168/ We study the growth and oscillation of , where and are entire functions of finite order not all vanishing identically and and are two linearly independent solutions of the linear differential equation . Zinelaâbidine Latreuch and Benharrat Belaïdi Copyright © 2013 Zinelaâbidine Latreuch and Benharrat Belaïdi. All rights reserved. Certain New Classes of Analytic Functions with Varying Arguments Wed, 30 Jan 2013 13:43:19 +0000 http://www.hindawi.com/journals/jca/2013/958210/ We introduce certain new classes and , which represent the κ uniformly starlike functions of order α and type β with varying arguments and the κ uniformly convex functions of order α and type β with varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes. R. M. El-Ashwah, M. K. Aouf, A. A. M. Hassan, and A. H. Hassan Copyright © 2013 R. M. El-Ashwah et al. All rights reserved. Starlikeness of General Integral Operator for Meromorphic Multivalent Functions Wed, 30 Jan 2013 11:39:44 +0000 http://www.hindawi.com/journals/jca/2013/690584/ We introduce a new integral operator for meromorphic multivalent functions. The starlikeness condition of this integral operator is determined. Several special cases are also discussed in the form of corollaries. Pranay Goswami and Serap Bulut Copyright © 2013 Pranay Goswami and Serap Bulut. All rights reserved. Normal Family of Meromorphic Functions concerning Shared Values Wed, 30 Jan 2013 11:37:47 +0000 http://www.hindawi.com/journals/jca/2013/107281/ We obtain a normal criterion of meromorphic functions concerning, shared values. Let be a family of meromorphic functions in a domain and let be positive integers. Let be two finite complex constants. If, for each , all zeros of have multiplicity at least and and share in for every pair of functions , then is normal in . This result generalizes the related theorem according to Xu et al. and Qi et al., respectively. There is a gap in the proofs of Lemma 3 by Wang (2012) and Theorem 1 by Zhang (2008), respectively. They did not consider the case of being zerofree. We will fill the gap in this paper. Wei Chen, Honggen Tian, Yingying Zhang, and Wenjun Yuan Copyright © 2013 Wei Chen et al. All rights reserved.