Journal of Complex Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Coefficient Estimates for a New Subclass of Analytic and Bi-Univalent 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 bi-univalent functions in the open unit disk . For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients and . Serap Bulut Copyright © 2014 Serap Bulut. All rights reserved. Certain Families of Multivalent Analytic Functions Associated with Iterations of the Owa-Srivastava 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 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. 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 sandwich-type 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 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.