International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations Thu, 17 Apr 2014 06:34:15 +0000 We present a new iterative method which does not involve inversion of the operators for obtaining an approximate solution for the nonlinear ill-posed operator equation . The proposed method is a modified form of Tikhonov gradient (TIGRA) method considered by Ramlau (2003). The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005). The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper. Ioannis K. Argyros, Santhosh George, and P. Jidesh Copyright © 2014 Ioannis K. Argyros et al. All rights reserved. Statistical Summability through de la Vallée-Poussin Mean in Probabilistic Normed Spaces Wed, 16 Apr 2014 06:15:27 +0000 Two concepts—one of statistical convergence and the other of de la Vallée-Poussin mean—play an important role in recent research on summability theory. In this work we define a new type of summability methods and statistical completeness involving the ideas of de la Vallée-Poussin mean and statistical convergence in the framework of probabilistic normed spaces. Ayhan Esi Copyright © 2014 Ayhan Esi. All rights reserved. On 3-Dimensional Contact Metric Generalized -Space Forms Tue, 15 Apr 2014 00:00:00 +0000 The present paper deals with a study of 3-dimensional contact metric generalized -space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized -space form with to be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric and -projectively flat, respectively. D. G. Prakasha, Shyamal Kumar Hui, and Kakasab Mirji Copyright © 2014 D. G. Prakasha et al. All rights reserved. Hessian Geometry on Lagrange Spaces Mon, 14 Apr 2014 09:42:51 +0000 We extend the correspondence between Hessian and Kähler metrics and curvatures to Lagrange spaces. Izu Vaisman Copyright © 2014 Izu Vaisman. All rights reserved. Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Mon, 14 Apr 2014 09:18:58 +0000 Let be an -dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere , and let and be the Blaschke tensor and the Möbius second fundamental form of , respectively. We define a symmetric tensor which is called the para-Blaschke tensor of , where is a constant. An eigenvalue of the para-Blaschke tensor is called a para-Blaschke eigenvalue of . The aim of this paper is to classify the oriented hypersurfaces in with two distinct para-Blaschke eigenvalues under some rigidity conditions. Junfeng Chen and Shichang Shu Copyright © 2014 Junfeng Chen and Shichang Shu. All rights reserved. Optimal Policies for Deteriorating Items with Maximum Lifetime and Two-Level Trade Credits Thu, 10 Apr 2014 12:45:34 +0000 The retailer’s optimal policies are developed when the product has fixed lifetime and also the units in inventory are subject to deterioration at a constant rate. This study will be mainly applicable to pharmaceuticals, drugs, beverages, and dairy products, and so forth. To boost the demand, offering a credit period is considered as the promotional tool. The retailer passes credit period to the buyers which is received from the supplier. The objective is to maximize the total profit per unit time of the retailer with respect to optimal retail price of an item and purchase quantity during the optimal cycle time. The concavity of the total profit per unit time is exhibited using inventory parametric values. The sensitivity analysis is carried out to advise the decision maker to keep an eye on critical inventory parameters. Nita H. Shah, Dushyantkumar G. Patel, and Digeshkumar B. Shah Copyright © 2014 Nita H. Shah et al. All rights reserved. Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of -Growth Wed, 09 Apr 2014 12:19:48 +0000 Let be a regular cone in and let be a tubular radial domain. Let be the convolutor in Beurling ultradistributions of -growth corresponding to . We define the Cauchy and Poisson integral of and show that the Cauchy integral of   is analytic in and satisfies a growth property. We represent   as the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation of . Also we show that the Poisson integral of corresponding to attains as boundary value in the distributional sense. Byung Keun Sohn Copyright © 2014 Byung Keun Sohn. All rights reserved. Approximation of Signals (Functions) by Trigonometric Polynomials in -Norm Wed, 09 Apr 2014 11:56:53 +0000 Mittal and Rhoades (1999, 2000) and Mittal et al. (2011) have initiated a study of error estimates through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix does not have monotone rows. In this paper, the first author continues the work in the direction for to be a -matrix. We extend two theorems on summability matrix of Deger et al. (2012) where they have extended two theorems of Chandra (2002) using -method obtained by deleting a set of rows from Cesàro matrix . Our theorems also generalize two theorems of Leindler (2005) to -matrix which in turn generalize the result of Chandra (2002) and Quade (1937). M. L. Mittal and Mradul Veer Singh Copyright © 2014 M. L. Mittal and Mradul Veer Singh. All rights reserved. Existence Theorems for Solvability of a Functional Equation Arising in Dynamic Programming Tue, 08 Apr 2014 07:31:07 +0000 The paper deals with the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming of multistage decision making processes in Banach spaces BC(S) and B(S) and complete metric space BB(S), respectively. Our main results extend, improve, and generalize the results due to several authors. Some examples are also given to demonstrate the advantage of our results over existing one in the literature. Deepmala Copyright © 2014 Deepmala. All rights reserved. Set-Valued Hardy-Rogers Type Contraction in 0-Complete Partial Metric Spaces Tue, 08 Apr 2014 00:00:00 +0000 In this paper we introduce set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces and prove the corresponding theorem of fixed point. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by Aydi et al. (2012). As an application of our results, a homotopy theorem for such mappings is derived. Also, some examples are included which show that our generalization is proper. Satish Shukla, Stojan Radenović, and Calogero Vetro Copyright © 2014 Satish Shukla et al. All rights reserved. Coproximinality in the Space of Bounded Functions Mon, 07 Apr 2014 12:09:44 +0000 As a counterpart to best approximation in Banach spaces, the best coapproximation was introduced by Franchetti and Furi (1972). In this paper, we shall consider the relation between coproximinality of a nonempty subset of a Banach space and of in . Eyad Abu-Sirhan and Zuhier Altawallbeh Copyright © 2014 Eyad Abu-Sirhan and Zuhier Altawallbeh. All rights reserved. Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function Sun, 06 Apr 2014 13:29:13 +0000 By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained. K. AL-Shaqsi Copyright © 2014 K. AL-Shaqsi. All rights reserved. Retracted: Partial Sums of Functions of Bounded Turning Thu, 03 Apr 2014 15:03:52 +0000 International Journal of Mathematics and Mathematical Sciences Copyright © 2014 International Journal of Mathematics and Mathematical Sciences. All rights reserved. A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting Thu, 03 Apr 2014 13:35:17 +0000 We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions. Christophe Chesneau Copyright © 2014 Christophe Chesneau. All rights reserved. On the Zweier Sequence Spaces of Fuzzy Numbers Thu, 03 Apr 2014 07:01:56 +0000 It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers , , and consisting of all sequences such that in the spaces , , and , respectively. Also, we prove that , , and are linearly isomorphic to the spaces , , and , respectively. Additionally, the -, -, and -duals of the spaces , , and have been computed. Furthermore, two theorems concerning matrix map have been given. Mehmet Şengönül Copyright © 2014 Mehmet Şengönül. All rights reserved. On the Structures of Abelian -Regular Rings Tue, 01 Apr 2014 08:48:33 +0000 Assume that is an Abelian ring. In this paper, we characterize the structure of whenever is -regular. It is also proved that an Abelian -regular ring is isomorphic to the subdirect sum of some metadivision rings. Jianwei Lu and Liguo He Copyright © 2014 Jianwei Lu and Liguo He. All rights reserved. A New Proof for the Description of Holomorphic Flows on Multiply Connected Domains Thu, 13 Mar 2014 09:59:01 +0000 We provide a new proof for the description of holomorphic and biholomorphic flows on multiply connected domains in the complex plane. In contrast to the original proof of Heins (1941) we do this by the means of operator theory and by utilizing the techniques of universal coverings of the underlying domains of holomorphic flows and their liftings on the corresponding universal coverings. F. Jafari, Z. Słodkowski, and T. Tonev Copyright © 2014 F. Jafari et al. All rights reserved. Jónsson and HS Modules over Commutative Rings Wed, 12 Mar 2014 06:44:56 +0000 Let be a commutative ring with identity and let be an infinite unitary -module. (Unless indicated otherwise, all rings are commutative with identity 1≠0 and all modules are unitary.) Then is called a Jónsson module provided every proper submodule of has smaller cardinality than . Dually, is said to be homomorphically smaller (HS for short) if for every nonzero submodule of . In this survey paper, we bring the reader up to speed on current research on these structures by presenting the principal results on Jónsson and HS modules. We conclude the paper with several open problems. Greg Oman Copyright © 2014 Greg Oman. All rights reserved. The Burkill-Cesari Integral on Spaces of Absolutely Continuous Games Mon, 10 Mar 2014 08:56:24 +0000 We prove that the Burkill-Cesari integral is a value on a subspace of and then discuss its continuity with respect to both the and the Lipschitz norm. We provide an example of value on a subspace of strictly containing as well as an existence result of a Lipschitz continuous value, different from Aumann and Shapley’s one, on a subspace of . F. Centrone and A. Martellotti Copyright © 2014 F. Centrone and A. Martellotti. All rights reserved. Some New Riemann-Liouville Fractional Integral Inequalities Mon, 10 Mar 2014 07:41:38 +0000 In this paper, some new fractional integral inequalities are established. Jessada Tariboon, Sotiris K. Ntouyas, and Weerawat Sudsutad Copyright © 2014 Jessada Tariboon et al. All rights reserved. Optimal Control Problem of Treatment for Obesity in a Closed Population Wed, 26 Feb 2014 15:48:50 +0000 Variety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obesity. A dynamical model for simulating the interaction between healthy people, overweight people, and obese people in a randomly mixed population is discussed in here. Two scenarios of intervention programs were implemented in the model, dietary program for overweight people with healthy life campaign and treatment program for obese people. Assuming all control rates are constant, disease free equilibrium point, endemic equilibrium point, and basic reproductive ratio () as the epidemic indicator were shown analytically. We find that the disease free equilibrium point is locally asymptotical stable if and only if . From sensitivity analysis of , we obtain that larger rate of dietary program and treatment program will reduce significantly. With control rates are continuous in time, an optimal control approach was applied into the model to find the best way to minimize the number of overweight and obese people. Some numerical analysis and simulations for optimal control of the intervention were shown to support the analytical results. D. Aldila, N. Rarasati, N. Nuraini, and E. Soewono Copyright © 2014 D. Aldila et al. All rights reserved. -Algebras Associated with Hilbert -Quad Modules of Finite Type Thu, 30 Jan 2014 10:15:16 +0000 A Hilbert -quad module of finite type has a multistructure of Hilbert -bimodules with two finite bases. We will construct a -algebra from a Hilbert -quad module of finite type and prove its universality subject to certain relations among generators. Some examples of the -algebras from Hilbert -quad modules of finite type will be presented. Kengo Matsumoto Copyright © 2014 Kengo Matsumoto. All rights reserved. The Height of a Class in the Cohomology Ring of Polygon Spaces Thu, 26 Dec 2013 14:56:10 +0000 Let be the configuration space of planar -gons having side lengths and modulo isometry group. For generic , the cohomology ring has a form where is the first Stiefel-Whitney class of a certain regular -cover and the ideal is in general big. For generic , we determine the number such that but . Yasuhiko Kamiyama and Kazufumi Kimoto Copyright © 2013 Yasuhiko Kamiyama and Kazufumi Kimoto. All rights reserved. A Solution to the Completion Problem for Quasi-Pseudometric Spaces Thu, 26 Dec 2013 14:03:18 +0000 The different notions of Cauchy sequence and completeness proposed in the literature for quasi-pseudometric spaces do not provide a satisfactory theory of completeness and completion for all quasi-pseudometric spaces. In this paper, we introduce a notion of completeness which is classical in the sense that it is made up of equivalence classes of Cauchy sequences and constructs a completion for any given quasi-pseudometric space. This new completion theory extends the existing completion theory for metric spaces and satisfies the requirements posed by Doitchinov for a nice theory of completeness. Athanasios Andrikopoulos Copyright © 2013 Athanasios Andrikopoulos. All rights reserved. Dimension Result for the Polynomial Algebra as a Module over the Steenrod Algebra Thu, 19 Dec 2013 15:36:47 +0000 For let be the polynomial algebra in variables of degree one, over the field of two elements. The mod-2 Steenrod algebra acts on according to well-known rules. Let denote the image of the action of the positively graded part of A major problem is that of determining a basis for the quotient vector space Both and are graded where denotes the set of homogeneous polynomials of degree A spike of degree is a monomial of the form where for each In this paper we show that if and can be expressed in the form with then where is the number of spikes of degree Mbakiso Fix Mothebe Copyright © 2013 Mbakiso Fix Mothebe. All rights reserved. Characterization of Banach Lattices in Terms of Quasi-Interior Points Wed, 27 Nov 2013 15:17:17 +0000 In terms of quasi-interior points, criteria that a Banach lattice has order continuous norm or is an -space with a unit are given. For example, if is Dedekind complete and has a weak order unit, then has order continuous norm if and only if the set of quasi-interior points of coincides with the set of weak order units of ; a Banach lattice is an -space with a unit if and only if the set of all quasi-interior points of coincides with the set . Analogous questions are considered for the case of an ordered Banach space with a cone . Moreover, it is shown that every nonzero point of a cone is quasi-interior if and only if . We also study various -properties of a cone ; in particular, the conditions for which the relation with implies that is not a quasi-interior point are considered. Egor A. Alekhno Copyright © 2013 Egor A. Alekhno. All rights reserved. Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized -Univex Functions Wed, 20 Nov 2013 09:13:54 +0000 We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized -univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized -univex functions. Jen-Chwan Liu and Chun-Yu Liu Copyright © 2013 Jen-Chwan Liu and Chun-Yu Liu. All rights reserved. Four-Point -Ary Interpolating Subdivision Schemes Thu, 14 Nov 2013 08:25:40 +0000 We present an efficient and simple algorithm to generate 4-point n-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-point n-ary interpolating schemes generated by completely different frameworks (i.e., Lagrange interpolant and wavelet theory) can also be generated by the proposed algorithm. Furthermore, we have discussed continuity, Hölder regularity, degree of polynomial generation, polynomial reproduction, and approximation order of the schemes. Ghulam Mustafa and Robina Bashir Copyright © 2013 Ghulam Mustafa and Robina Bashir. All rights reserved. Left Baire-1 Compositors and Continuous Functions Wed, 06 Nov 2013 14:36:08 +0000 We showed that the class of left Baire-1 compositors is precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative the conjecture in the work by Fenecios and Cabral (2012, page 43). Moreover, based on the above result we provide a new proof that the class of functions where is the class of all positive continuous functions and is the class of all positive constants as defined in the work by Bakowska and Pawlak (2010) is exactly the class of all continuous functions. Jonald P. Fenecios and Emmanuel A. Cabral Copyright © 2013 Jonald P. Fenecios and Emmanuel A. Cabral. All rights reserved. Noncompact Perturbation of Sweeping Process with Delay in Banach Spaces Thu, 31 Oct 2013 15:34:28 +0000 We have proven an existence theorem concerning the existence of solutions for a functional evolution inclusion governed by sweeping process with closed convex sets depending on time and state and with a noncompact nonconvex perturbation in Banach spaces. This work extends some recent existence theorems concerning sweeping processes from Hilbert spaces setting to Banach spaces setting. Moreover, it improves some recent existence results for sweeping processes in Banach spaces. F. Aladsani and A. G. Ibrahim Copyright © 2013 F. Aladsani and A. G. Ibrahim. All rights reserved.