Journal of Complex Analysis The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh -Differential Operator Tue, 05 Sep 2017 08:26:15 +0000 We introduce in our present investigation a new subclass of analytic and biunivalent functions associated with Ruscheweyh -differential operator in open unit disk . We use the Faber polynomial expansions to find th coefficients bounds of class of bisubordinate functions and also find initial coefficient estimates. Saqib Hussain, Shahid Khan, Muhammad Asad Zaighum, Maslina Darus, and Zahid Shareef Copyright © 2017 Saqib Hussain et al. All rights reserved. Uniformly Geometric Functions Involving Constructed Operators Sun, 16 Apr 2017 07:53:20 +0000 This paper introduces classes of uniformly geometric functions involving constructed differential operators by means of convolution. Basic properties of those classes are studied, namely, coefficient bounds and inclusion relations. Mohammad Al-Kaseasbeh and Maslina Darus Copyright © 2017 Mohammad Al-Kaseasbeh and Maslina Darus. All rights reserved. On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci Tue, 28 Mar 2017 00:00:00 +0000 A connected real analytic hypersurface whose Levi form is nondegenerate in at least one point—hence at every point of some Zariski-dense open subset—is locally biholomorphic to the model Heisenberg quadric pseudosphere of signature in one point if and only if, at every other Levi nondegenerate point, it is also locally biholomorphic to some Heisenberg pseudosphere, possibly having a different signature . Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any. Joël Merker Copyright © 2017 Joël Merker. All rights reserved. Basic Sets of Special Monogenic Polynomials in Fréchet Modules Tue, 14 Feb 2017 00:00:00 +0000 This article is concerned with the study of the theory of basic sets in Fréchet modules in Clifford analysis. The main aim of this account, which is based on functional analysis consideration, is to formulate criteria of general type for the effectiveness (convergence properties) of basic sets either in the space itself or in a subspace of finer topology. By attributing particular forms for the Fréchet module of different classes of functions, conditions are derived from the general criteria for the convergence properties in open and closed balls. Our results improve and generalize some known results in complex and Clifford setting concerning the effectiveness of basic sets. Gamal Farghaly Hassan, Lassaad Aloui, and Allal Bakali Copyright © 2017 Gamal Farghaly Hassan et al. All rights reserved. Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation Tue, 06 Sep 2016 14:14:38 +0000 Let denote the family of functions of bounded boundary rotation so that in the open unit disk . We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions . V. Radhika, S. Sivasubramanian, G. Murugusundaramoorthy, and Jay M. Jahangiri Copyright © 2016 V. Radhika et al. All rights reserved. Approximate Conformal Mappings and Elasticity Theory Sun, 28 Aug 2016 09:56:10 +0000 Here, we present the new method of approximate conformal mapping of the unit disk to a one-connected domain with smooth boundary without auxiliary constructions and iterations. The mapping function is a Taylor polynomial. The method is applicable to elasticity problems solution. Pyotr N. Ivanshin and Elena A. Shirokova Copyright © 2016 Pyotr N. Ivanshin and Elena A. Shirokova. All rights reserved. Generalized Relative Type and Generalized Weak Type of Entire Functions Wed, 13 Jul 2016 14:17:24 +0000 We study some relative growth properties of entire functions with respect to another entire function on the basis of generalized relative type and generalized relative weak type. Sanjib Kumar Datta, Tanmay Biswas, and Debasmita Dutta Copyright © 2016 Sanjib Kumar Datta et al. All rights reserved. Complex Valued -Metric Spaces and Common Fixed Point Theorems under Rational Contractions Mon, 27 Jun 2016 07:09:20 +0000 The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued -metric space. The obtained results generalize and extend some of the well-known results in the literature. Anil Kumar Dubey Copyright © 2016 Anil Kumar Dubey. All rights reserved. Dirichlet Problem for Complex Poisson Equation in a Half Hexagon Domain Wed, 10 Feb 2016 11:47:26 +0000 The parqueting-reflection 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 Cone-Type Planar Domains Wed, 10 Feb 2016 07:57:14 +0000 We establish sharp estimates for Green’s functions of cone-type 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 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 King’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 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 Carlson-Shaffer Operator and Related to Lemniscate of Bernoulli Tue, 16 Dec 2014 06:35:11 +0000 The object of the present investigation is to solve the Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new class of analytic functions involving the Carlson-Shaffer 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 Bi-Univalent Functions Defined by Hadamard Product Mon, 10 Nov 2014 12:03:00 +0000 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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.