ISRN Mathematical Analysis The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Some Inequalities for Polynomials Not Vanishing inside a Circle Mon, 19 May 2014 09:24:39 +0000 If is a polynomial of degree having no zeros in , then it is known that, for all with , , , and , . In this paper, we will prove a result which not only generalizes the above inequality but also generalize and refines the various results pertaining to the norm of . We will also prove a result which extends and refines a result of Boas Jr. and Rahman (1962). Also we will see that our results lead to some striking conclusions giving refinements and generalizations of other well-known results. Abdullah Mir and Bilal Dar Copyright © 2014 Abdullah Mir and Bilal Dar. All rights reserved. Hamburger and Stieltjes Moment Problems for Operators Wed, 30 Apr 2014 09:14:50 +0000 Solutions to some operator-valued, unidimensional, Hamburger and Stieltjes moment problems in this paper are given. Necessary and sufficient conditions on some sequences of bounded operators being Hamburger, respectively, Stieltjes operator-valued moment sequences are obtained. The determinateness of the operator-valued Hamburger and Stieltjes moment sequence is studied. L. Lemnete-Ninulescu Copyright © 2014 L. Lemnete-Ninulescu. All rights reserved. On the Sumudu Transform and Its Extension to a Class of Boehmians Thu, 24 Apr 2014 06:45:58 +0000 Boehmians are used for all objects obtained by an algebraic construction similar to that of the field of quotients. In literature, several integral transforms have been extended to various Boehmian spaces but a few to the space of strong Boehmians. As shown in the work of Al-Omari (2013), this work describes certain spaces of Boehmians. The Sumudu transform is therefore established and it is one-one and continuous in the space of Boehmians. The inverse transform is given and some results are also discussed. S. K. Q. Al-Omari Copyright © 2014 S. K. Q. Al-Omari. All rights reserved. Approximation by -Transformation of Double Walsh-Fourier Series to Multivariable Functions Tue, 22 Apr 2014 13:11:29 +0000 We study the Walsh series expansion of multivariate functions in and, in particular, in . The rate of uniform approximation by T-transformation of rectangular partial sums of double Walsh to these functions is investigated. By extending the concepts of rest (head) bounded variation series, which was introduced by Leindler (2004), we generalize the related results of Móricz and Rhoades (1996), Nagy (2012). Our results can be applied to many summability methods, including the Nörlund summability and weighted summability. Yi Zhao and Dansheng Yu Copyright © 2014 Yi Zhao and Dansheng Yu. All rights reserved. Contiguous Function Relations for -Hypergeometric Functions Thu, 10 Apr 2014 08:36:43 +0000 In this research work, our aim is to determine the contiguous function relations for -hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also obtain contiguous function relations for two parameters. Throughout in this research paper, we find out the contiguous function relations for both the cases in terms of a new parameter . Obviously if , then the contiguous function relations for -hypergeometric functions are Gauss contiguous function relations. Shahid Mubeen, Gauhar Rahman, Abdur Rehman, and Mammona Naz Copyright © 2014 Shahid Mubeen et al. All rights reserved. Meromorphic Parabolic Starlike Functions Associated with -Hypergeometric Series Mon, 07 Apr 2014 08:00:57 +0000 We introduce a new class of meromorphic parabolic starlike functions with a fixed point defined in the punctured unit disk involving the -hypergeometric functions. We obtained coefficient inequalities, growth and distortion inequalities, and closure results for functions . We further established some results concerning convolution and the partial sums. G. Murugusundaramoorthy and T. Janani Copyright © 2014 G. Murugusundaramoorthy and T. Janani. All rights reserved. An Alternate Proof of the De Branges Theorem on Canonical Systems Thu, 03 Apr 2014 08:36:39 +0000 The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on . This provides an alternative proof of the De Branges theorem that the canonical systems with imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system. Keshav Raj Acharya Copyright © 2014 Keshav Raj Acharya. All rights reserved. Global Existence of Solution for Cauchy Problem of Two-Dimensional Boussinesq-Type Equation Thu, 27 Mar 2014 11:13:14 +0000 In this paper, we consider the Cauchy problem of two-dimensional Boussinesq-type equations . Under the assumptions that is a function with exponential growth at infinity and under some assumptions on the initial data, we prove the existence of global weak solution. Qingying Hu, Chenxia Zhang, and Hongwei Zhang Copyright © 2014 Qingying Hu et al. All rights reserved. A Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Space Wed, 26 Mar 2014 00:00:00 +0000 We prove the existence of a weak solution for the degenerate nonlinear elliptic Dirichlet boundary-value problem in , on , in a suitable weighted Sobolev space, where is a bounded domain and is a continuous bounded nonlinearity. Rasmita Kar Copyright © 2014 Rasmita Kar. All rights reserved. A Formula for the Numerical Range of Elementary Operators Thu, 20 Mar 2014 07:02:20 +0000 Let be the algebra of bounded linear operators on a complex Hilbert space . For -tuples of elements of and , let denote the elementary operator on defined by . In this paper, we prove the following formula for the numerical range of : , where is the set of unitary operators. M. Barraa Copyright © 2014 M. Barraa. All rights reserved. Stability of Hybrid Stochastic Systems with Time-Delay Mon, 17 Mar 2014 09:50:36 +0000 This paper develops some criteria for a kind of hybrid stochastic systems with time-delay, which improve existing results on hybrid systems without considering noises. The improved results show that the presence of noise is quite involved in the stability analysis of hybrid systems. New results can be used to analyze the stability of a kind of stochastic hybrid impulsive and switching neural networks (SHISNN). Therefore, stability analysis of SHISNN can be turned into solving a linear matrix inequality (LMI). Pu Xing-cheng and Yuan Wei Copyright © 2014 Pu Xing-cheng and Yuan Wei. All rights reserved. Some Applications of Second-Order Differential Subordination on a Class of Analytic Functions Defined by Komatu Integral Operator Wed, 12 Mar 2014 08:06:46 +0000 We introduce a new class of analytic functions by using Komatu integral operator and obtain some subordination results. Serap Bulut Copyright © 2014 Serap Bulut. All rights reserved. Hermite Interpolation on the Unit Circle Considering up to the Second Derivative Mon, 10 Mar 2014 14:25:27 +0000 The paper is devoted to study the Hermite interpolation problem on the unit circle. The interpolation conditions prefix the values of the polynomial and its first two derivatives at the nodal points and the nodal system is constituted by complex numbers equally spaced on the unit circle. We solve the problem in the space of Laurent polynomials by giving two different expressions for the interpolation polynomial. The first one is given in terms of the natural basis of Laurent polynomials and the remarkable fact is that the coefficients can be computed in an easy and efficient way by means of the Fast Fourier Transform (FFT). The second expression is a barycentric formula, which is very suitable for computational purposes. Elías Berriochoa, Alicia Cachafeiro, and Jaime Díaz Copyright © 2014 Elías Berriochoa et al. All rights reserved. Self-Adjoint Extension and Spectral Theory of a Linear Relation in a Hilbert Space Wed, 05 Mar 2014 06:34:29 +0000 The aim of this paper is to develop the conditions for a symmetric relation in a Hilbert space ℋ to have self-adjoint extensions in terms of defect indices and discuss some spectral theory of such linear relation. Keshav Raj Acharya Copyright © 2014 Keshav Raj Acharya. All rights reserved. On the Fekete-Szegö Problem for a Class of Analytic Functions Tue, 04 Mar 2014 13:43:31 +0000 Let denote the class of functions which are analytic in the unit disk and given by the power series . Let be the class of convex functions. In this paper, we give the upper bounds of for all real number and for any in the family , Re for  some . Zhigang Peng Copyright © 2014 Zhigang Peng. All rights reserved. A Regularization Method for the Elliptic Equation with Inhomogeneous Source Tue, 04 Mar 2014 09:51:02 +0000 We consider the following Cauchy problem for the elliptic equation with inhomogeneous source in a rectangular domain with Dirichlet boundary conditions at and . The problem is ill-posed. The main aim of this paper is to introduce a regularization method and use it to solve the problem. Some sharp error estimates between the exact solution and its regularization approximation are given and a numerical example shows that the method works effectively. Tuan H. Nguyen and Binh Thanh Tran Copyright © 2014 Tuan H. Nguyen and Binh Thanh Tran. All rights reserved. Homoclinic Orbits for a Class of Subquadratic Second Order Hamiltonian Systems Tue, 04 Mar 2014 00:00:00 +0000 The existence and multiplicity of homoclinic orbits are considered for a class of subquadratic second order Hamiltonian systems . Recent results from the literature are generalized and significantly improved. Examples are also given in this paper to illustrate our main results. Li-Li Wan Copyright © 2014 Li-Li Wan. All rights reserved. Multiple Periodic Solutions of Generalized Gause-Type Predator-Prey Systems with Nonmonotonic Numerical Responses and Impulse Mon, 17 Feb 2014 15:34:56 +0000 We consider an impulsive periodic generalized Gause-type predator-prey model with nonmonotonic numerical responses. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results extend and improve some known criteria. Zhenguo Luo, Liping Luo, and Yunhui Zeng Copyright © 2014 Zhenguo Luo et al. All rights reserved. Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent Wed, 12 Feb 2014 12:41:05 +0000 The paper establishes some sufficient conditions for the boundedness of singular integral operators and their commutators from products of variable exponent Herz spaces to variable exponent Herz spaces. Amjad Hussain and Guilian Gao Copyright © 2014 Amjad Hussain and Guilian Gao. All rights reserved. Existence of Nontrivial Solutions of p-Laplacian Equation with Sign-Changing Weight Functions Wed, 12 Feb 2014 07:09:01 +0000 This paper shows the existence and multiplicity of nontrivial solutions of the p-Laplacian problem for with zero Dirichlet boundary conditions, where is a bounded open set in , if , if ), , is a smooth function which may change sign in , and . The method is based on Nehari results on three submanifolds of the space . Ghanmi Abdeljabbar Copyright © 2014 Ghanmi Abdeljabbar. All rights reserved. Hilbert Transforms along Convex Curves for -Valued Functions Thu, 06 Feb 2014 12:45:45 +0000 We show that Hilbert transforms along a large class of convex curves are bounded on , where , . Honghai Liu Copyright © 2014 Honghai Liu. All rights reserved. A Priori Estimation of the Solution for Mixed Problems with Integral Condition for Singular Parabolic Equations Tue, 04 Feb 2014 07:24:46 +0000 We prove a theorem in which we get a priori estimation of the solution for mixed problems with integral condition for singular parabolic equations. Mixed problems with nonlocal boundary conditions or with nonlocal initial conditions were studied in many works lately. Our result plays an important role in the theory of heat transmission, thermoelasticity, chemical engineering, underground water flow, and plasma physics. Raid Almomani Copyright © 2014 Raid Almomani. All rights reserved. Convolution Properties of a Subclass of Analytic Univalent Functions Sun, 02 Feb 2014 13:09:17 +0000 The main objective of the present paper is to investigate some interesting properties on convolution and generalized convolution of functions for the classes and . Our results improve the results of previous authors. Saurabh Porwal Copyright © 2014 Saurabh Porwal. All rights reserved. Potra-Pták Iterative Method with Memory Wed, 22 Jan 2014 12:41:56 +0000 The problem is to extend the method proposed by Soleymani et al. (2012) to a method with memory. Following this aim, a free parameter is calculated using Newton’s interpolatory polynomial of the third degree. So the R-order of convergence is increased from 4 to 6 without any new function evaluations. Numerically the extended method is examined along with comparison to some existing methods with the similar properties. Taher Lotfi, Stanford Shateyi, and Sommayeh Hadadi Copyright © 2014 Taher Lotfi et al. All rights reserved. Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type Sun, 05 Jan 2014 07:37:34 +0000 The approximation characteristics of trigonometric sums of special type on the class of ()-differentiable (in the sense of A. I. Stepanets) periodical functions are studied. Because of agreement between parameters of approximative sums and approximated classes, the solution of Kolmogorov-Nikol’skii problem is obtained in a sufficiently general case. It is shown that in a number of important cases these sums provide higher order of approximation in comparison with Fourier sums, de la Vallée Poussin sums, and others on the class in the uniform metric. The range of parameters in which the sums give the order of the best uniform approximation on the classes is indicated. A. S. Serdyuk and Ie. Yu. Ovsii Copyright © 2014 A. S. Serdyuk and Ie. Yu. Ovsii. All rights reserved. The Radon Transforms on the Generalized Heisenberg Group Thu, 02 Jan 2014 15:12:21 +0000 Let be the generalized Heisenberg group. In this paper, we study the inversion of the Radon transforms on . Several kinds of inversion Radon transform formulas are established. One is obtained from the Euclidean Fourier transform; the other is derived from the differential operator with respect to the center variable . Also by using sub-Laplacian and generalized sub-Laplacian we deduce an inversion formula of the Radon transform on . Tianwu Liu and Jianxun He Copyright © 2014 Tianwu Liu and Jianxun He. All rights reserved. Existence of Positive Solutions for Fourth-Order Boundary Value Problems with Sign-Changing Nonlinear Terms Tue, 19 Nov 2013 15:32:55 +0000 the existence of positive solutions for a fourth-order boundary value problem with a sign-changing nonlinear term is investigated. By using Krasnoselskii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained. An example is presented to illustrate the application of our main results. Xingfang Feng and Hanying Feng Copyright © 2013 Xingfang Feng and Hanying Feng. All rights reserved. Endpoints of Multivalued Contraction Operators Sun, 17 Nov 2013 10:02:54 +0000 The existence of the endpoints and approximate endpoints are studied in a general setting for the operators satisfying various contractive conditions. Some recent results are also derived as special cases. Bhagwati Prasad and Ritu Sahni Copyright © 2013 Bhagwati Prasad and Ritu Sahni. All rights reserved. Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with -Laplacian Operator Sun, 10 Nov 2013 09:19:10 +0000 This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with -Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective. Xiangshan Kong and Haitao Li Copyright © 2013 Xiangshan Kong and Haitao Li. All rights reserved. A New Existence Theory for Positive Periodic Solutions to a Class of Neutral Delay Model with Feedback Control and Impulse Tue, 05 Nov 2013 14:03:34 +0000 We acquire some sufficient and realistic conditions for the existence of positive periodic solution of a general neutral impulsive -species competitive model with feedback control by applying some analysis techniques and a new existence theorem, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for -set contraction. As applications, we also examine some special cases, which have been studied extensively in the literature, some known results are improved and generalized. Zhenguo Luo, Jianhua Huang, and Binxiang Dai Copyright © 2013 Zhenguo Luo et al. All rights reserved.