Journal of Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics Mon, 15 Sep 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/569719/ The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient. Anuradha Singh and J. P. Jaiswal Copyright © 2014 Anuradha Singh and J. P. Jaiswal. All rights reserved. Some Inequalities for the Derivative of Polynomials Sun, 14 Sep 2014 09:49:32 +0000 http://www.hindawi.com/journals/jmath/2014/160485/ If is a polynomial of degree , having no zeros in , then Aziz (1989) proved , where . In this paper, we consider a class of polynomial of degree , defined as and present certain generalizations of above inequality and some other well-known results. Sunil Hans, Dinesh Tripathi, and Babita Tyagi Copyright © 2014 Sunil Hans et al. All rights reserved. -Regular Sets in Topology and Generalized Topology Sun, 14 Sep 2014 07:33:50 +0000 http://www.hindawi.com/journals/jmath/2014/274592/ We define and study a new class of regular sets called -regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using -regular sets. Semiconnectedness is characterized by using -regular sets. -continuity and almost -continuity are introduced and investigated. Ankit Gupta and Ratna Dev Sarma Copyright © 2014 Ankit Gupta and Ratna Dev Sarma. All rights reserved. Inverse Limit Spaces with Various Shadowing Property Sun, 14 Sep 2014 07:11:56 +0000 http://www.hindawi.com/journals/jmath/2014/169183/ We discuss the relationship between ergodic shadowing property and inverse shadowing property of and that of the shift map σf on the inverse limit space. Ali Barzanouni Copyright © 2014 Ali Barzanouni. All rights reserved. Montgomery Identity and Ostrowski Type Inequalities for Riemann-Liouville Fractional Integral Wed, 10 Sep 2014 13:21:31 +0000 http://www.hindawi.com/journals/jmath/2014/503195/ We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a function with respect to another function . We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong to spaces. These inequalities are generally sharp in case and the best possible in case . Application for Hadamard fractional integrals is given. Andrea Aglić Aljinović Copyright © 2014 Andrea Aglić Aljinović. All rights reserved. A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems Tue, 09 Sep 2014 07:23:17 +0000 http://www.hindawi.com/journals/jmath/2014/560578/ We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is very effective and efficient. Yuan Li, Hai-Shan Han, and Dan-Dan Yang Copyright © 2014 Yuan Li et al. All rights reserved. On Some New Generalized Difference Sequence Spaces of Nonabsolute Type Tue, 09 Sep 2014 06:19:20 +0000 http://www.hindawi.com/journals/jmath/2014/876813/ We define a new triangle matrix by the composition of the matrices and . Also, we introduce the sequence spaces , and by using matrix domain of the matrix on the classical sequence spaces , and , respectively, where . Moreover, we show that the space is norm isomorphic to for . Furthermore, we establish some inclusion relations concerning those spaces and determine -, -, and -duals of those spaces and construct the Schauder bases , and . Finally, we characterize the classes of infinite matrices where and . Osman Duyar, Serkan Demiriz, and Osman Özdemir Copyright © 2014 Osman Duyar et al. All rights reserved. A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space Mon, 08 Sep 2014 10:59:33 +0000 http://www.hindawi.com/journals/jmath/2014/713690/ Spectral properties of a special class of infinite dimensional Dirac operators on the abstract boson-fermion Fock space associated with the pair of complex Hilbert spaces are investigated, where is a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operator is taken to be a free infinite dimensional Dirac operator. A variety of the kernel of is shown. It is proved that there are cases where, for all sufficiently large with , has infinitely many nonzero eigenvalues even if has no nonzero eigenvalues. Also Fredholm property of restricted to a subspace of is discussed. Asao Arai Copyright © 2014 Asao Arai. All rights reserved. New Interpretations of Cohen’s Kappa Wed, 03 Sep 2014 06:21:10 +0000 http://www.hindawi.com/journals/jmath/2014/203907/ Cohen’s kappa is a widely used association coefficient for summarizing interrater agreement on a nominal scale. Kappa reduces the ratings of the two observers to a single number. With three or more categories it is more informative to summarize the ratings by category coefficients that describe the information for each category separately. Examples of category coefficients are the sensitivity or specificity of a category or the Bloch-Kraemer weighted kappa. However, in many research studies one is often only interested in a single overall number that roughly summarizes the agreement. It is shown that both the overall observed agreement and Cohen’s kappa are weighted averages of various category coefficients and thus can be used to summarize these category coefficients. Matthijs J. Warrens Copyright © 2014 Matthijs J. Warrens. All rights reserved. Self-Dual Normal Basis of a Galois Ring Mon, 01 Sep 2014 12:40:57 +0000 http://www.hindawi.com/journals/jmath/2014/258187/ Let and be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for over , where is considered as a free module over . Moreover, we explain a way to construct self-dual normal basis using particular system of polynomials. Finally, we show the connection between self-dual normal basis for over and the set of all invertible, circulant, and orthogonal matrices over . Irwansyah, Intan Muchtadi-Alamsyah, Aleams Barra, and Ahmad Muchlis Copyright © 2014 Irwansyah et al. All rights reserved. Basicity of the System of Exponents with a Linear Phase in Sobolev Weight Space Mon, 01 Sep 2014 09:57:34 +0000 http://www.hindawi.com/journals/jmath/2014/481425/ In the present paper a criterion for basicity of exponential system with linear phase is obtained in Sobolev weight space . Togrul Muradov and Valid Salmanov Copyright © 2014 Togrul Muradov and Valid Salmanov. All rights reserved. Weight Distribution of Periodic Errors and Optimal/Anti-Optimal Linear Codes Sun, 31 Aug 2014 08:12:46 +0000 http://www.hindawi.com/journals/jmath/2014/971410/ The paper discusses weight distribution of periodic errors and then the optimal case on bounds of parity check digits for (, ) linear codes over that corrects all periodic errors of order in the first block of length and all periodic errors of order in the second block of length and no others. Further, we extend the study to the case when the errors are in the form of periodic errors of order (and ) or more in the two subblocks. Pankaj Kumar Das Copyright © 2014 Pankaj Kumar Das. All rights reserved. A Note on Lax Pairs of the Sawada-Kotera Equation Sun, 24 Aug 2014 12:04:31 +0000 http://www.hindawi.com/journals/jmath/2014/906165/ We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to each other if and only if the spectral parameter is nonzero, while for zero spectral parameter a nongauge transformation is required. Sergei Sakovich Copyright © 2014 Sergei Sakovich. All rights reserved. On Some Grüss-Type Fractional Inequalities Using Saigo Fractional Integral Operator Sun, 24 Aug 2014 09:44:14 +0000 http://www.hindawi.com/journals/jmath/2014/527910/ The main aim of this paper is to establish some new fractional integral inequalities of Grüss-type via the Saigo fractional integral operator. Vaijanath L. Chinchane and Deepak B. Pachpatte Copyright © 2014 Vaijanath L. Chinchane and Deepak B. Pachpatte. All rights reserved. On Iterated Entire Functions with ()th Order Sun, 17 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/908798/ We prove some results relating to the comparative growth properties of iterated entire functions using (p, q)th order ((p, q)th lower order). Sanjib Kumar Datta, Tanmay Biswas, and Chinmay Biswas Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved. Associate, Hyperdomainlike, and Presimplifiable Hyperrings Thu, 14 Aug 2014 13:27:03 +0000 http://www.hindawi.com/journals/jmath/2014/458603/ Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented. Agboola Adesina Abdul Akeem and Davvaz Bijan Copyright © 2014 Agboola Adesina Abdul Akeem and Davvaz Bijan. All rights reserved. A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications Wed, 13 Aug 2014 13:04:03 +0000 http://www.hindawi.com/journals/jmath/2014/838497/ We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals. Hui Bao and Xingdi Chen Copyright © 2014 Hui Bao and Xingdi Chen. All rights reserved. Solving Systems of Volterra Integral and Integrodifferential Equations with Proportional Delays by Differential Transformation Method Tue, 12 Aug 2014 09:17:18 +0000 http://www.hindawi.com/journals/jmath/2014/725648/ In this paper, the differential transformation method is applied to the system of Volterra integral and integrodifferential equations with proportional delays. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series forms. If the solutions of the problem can be expanded to Taylor series, then the method gives opportunity to determine the coefficients of Taylor series. Hence, the exact solution can be obtained in Taylor series form. In illustrative examples, the method is applied to a few types of systems. Şuayip Yüzbaşı and Nurbol Ismailov Copyright © 2014 Şuayip Yüzbaşı and Nurbol Ismailov. All rights reserved. Complete Invariance Property with respect to Homeomorphism over Frame Multiwavelet and Super-Wavelet Spaces Mon, 04 Aug 2014 08:27:23 +0000 http://www.hindawi.com/journals/jmath/2014/528342/ We discuss the complete invariance property with respect to homeomorphism (CIPH) over various sets of wavelets containing all orthonormal multiwavelets, all tight frame multiwavelets, all super-wavelets of length n, and all normalized tight super frame wavelets of length n. Saurabh Chandra Maury Copyright © 2014 Saurabh Chandra Maury. All rights reserved. Harmonic Subtangent Structures Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/603078/ The concept of harmonic subtangent structures on almost subtangent metric manifolds is introduced and a Bochner-type formula is proved for this case. Conditions for a subtangent harmonic structure to be preserved by harmonic maps are also given. Adara M. Blaga Copyright © 2014 Adara M. Blaga. All rights reserved. Remarks on Homogeneous Al-Salam and Carlitz Polynomials Thu, 17 Jul 2014 08:15:02 +0000 http://www.hindawi.com/journals/jmath/2014/523013/ Several multilinear generating functions of the homogeneous Al-Salam and Carlitz polynomials are derived from -operator. In addition, two interesting relationships of product of this kind of polynomials are obtained. Jian-Ping Fang Copyright © 2014 Jian-Ping Fang. All rights reserved. On Generalized Derivations of BCI-Algebras and Their Properties Wed, 16 Jul 2014 12:03:00 +0000 http://www.hindawi.com/journals/jmath/2014/207161/ We introduce the concept of -derivations of BCI-algebras and we investigate some fundamental properties and establish some results on -derivations. Also, we treat to generalization of right derivation and left derivation of BCI-algebras and consider some related properties. L. Kamali Ardekani and B. Davvaz Copyright © 2014 L. Kamali Ardekani and B. Davvaz. All rights reserved. Novel Properties of Fuzzy Labeling Graphs Wed, 09 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/375135/ The concepts of fuzzy labeling and fuzzy magic labeling graph are introduced. Fuzzy magic labeling for some graphs like path, cycle, and star graph is defined. It is proved that every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. We have shown that the removal of a fuzzy bridge from a fuzzy magic cycle with odd nodes reduces the strength of a fuzzy magic cycle. Some properties related to fuzzy bridge and fuzzy cut node have also been discussed. A. Nagoor Gani, Muhammad Akram, and D. Rajalaxmi (a) Subahashini Copyright © 2014 A. Nagoor Gani et al. All rights reserved. Asymptotic Law of the th Records in the Bivariate Exponential Case Tue, 08 Jul 2014 07:17:56 +0000 http://www.hindawi.com/journals/jmath/2014/458914/ We consider a sequence of independent and identically distributed random variables with joint cumulative distribution , which has exponential marginals and with parameter . We also assume that , , and . We denote and by the sequences of the th records in the sequences , , respectively. The main result of of the paper is to prove the asymptotic independence of and using the property of stopping time of the th record times and that of the exponential distribution. Grine Azedine Copyright © 2014 Grine Azedine. All rights reserved. Startpoints and -Contractions in Quasi-Pseudometric Spaces Wed, 02 Jul 2014 09:34:29 +0000 http://www.hindawi.com/journals/jmath/2014/709253/ We introduce the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued maps. Yaé Ulrich Gaba Copyright © 2014 Yaé Ulrich Gaba. All rights reserved. Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales Tue, 01 Jul 2014 09:19:19 +0000 http://www.hindawi.com/journals/jmath/2014/965097/ Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equation . In order to improve the error estimate available by Vasin and George (2013), in the present paper we extend the iterative method considered by Vasin and George (2013), in the setting of Hilbert scales. The error estimates obtained under a general source condition on ( is the initial guess and is the actual solution), using the adaptive scheme proposed by Pereverzev and Schock (2005), are of optimal order. The algorithm is applied to numerical solution of an integral equation in Numerical Example section. Monnanda Erappa Shobha and Santhosh George Copyright © 2014 Monnanda Erappa Shobha and Santhosh George. All rights reserved. Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions Thu, 19 Jun 2014 08:32:34 +0000 http://www.hindawi.com/journals/jmath/2014/346305/ A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given. İmdat İşcan Copyright © 2014 İmdat İşcan. All rights reserved. Euler Type Integrals and Integrals in Terms of Extended Beta Function Thu, 12 Jun 2014 00:00:00 +0000 http://www.hindawi.com/journals/jmath/2014/686324/ We derive the evaluations of certain integrals of Euler type involving generalized hypergeometric series. Further, we establish a theorem on extended beta function, which provides evaluation of certain integrals in terms of extended beta function and certain special polynomials. The possibility of extending some of the derived results to multivariable case is also investigated. Subuhi Khan and Mustafa Walid Al-Saad Copyright © 2014 Subuhi Khan and Mustafa Walid Al-Saad. All rights reserved. Inclusion Properties of Certain Subclasses of -Valent Functions Associated with the Integral Operator Thu, 29 May 2014 06:03:29 +0000 http://www.hindawi.com/journals/jmath/2014/749251/ The purpose of the present paper is to introduce two subclasses of -valent functions by using the integral operator and to investigate various properties for these subclasses. Tamer M. Seoudy Copyright © 2014 Tamer M. Seoudy. All rights reserved. Shape Preserving Properties for -Bernstein-Stancu Operators Mon, 05 May 2014 06:43:22 +0000 http://www.hindawi.com/journals/jmath/2014/603694/ We investigate shape preserving for -Bernstein-Stancu polynomials introduced by Nowak in 2009. When , reduces to the well-known -Bernstein polynomials introduced by Phillips in 1997; when , reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; when , , we obtain classical Bernstein polynomials. We prove that basic basis is a normalized totally positive basis on and -Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on . Yali Wang and Yinying Zhou Copyright © 2014 Yali Wang and Yinying Zhou. All rights reserved.