Chinese Journal of Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Few Inequalities Established by Using Fractional Calculus and Their Applications to Certain Multivalently Analytic Functions Wed, 18 Jun 2014 09:37:02 +0000 http://www.hindawi.com/journals/cjm/2014/349719/ By making use of different techniques given in Miller and Mocanu (2000) (and also in Jack (1971)), some recent results consisting of certain multivalently analytic functions given both in Irmak (2005) and in Irmak (2010) are firstly restated and some of their applications are then pointed out. Hüseyin Irmak Copyright © 2014 Hüseyin Irmak. All rights reserved. Existence and Multiplicity of Positive Solutions for a System of Fourth-Order Boundary Value Problems Wed, 18 Jun 2014 06:26:37 +0000 http://www.hindawi.com/journals/cjm/2014/717290/ We study the existence and multiplicity of positive solutions for the system of fourth-order boundary value problems , and where . We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and inequalities and -monotone matrices. Shoucheng Yu and Zhilin Yang Copyright © 2014 Shoucheng Yu and Zhilin Yang. All rights reserved. On Hermite-Hadamard Type Inequalities for Riemann-Liouville Fractional Integrals via Two Kinds of Convexity Sun, 15 Jun 2014 09:28:29 +0000 http://www.hindawi.com/journals/cjm/2014/173293/ We obtain some Hermite-Hadamard type inequalities for products of two -convex functions via Riemann-Liouville integrals. The analogous results for -convex functions are also established. Feixiang Chen Copyright © 2014 Feixiang Chen. All rights reserved. Linear Independent Solutions and Operational Representations for Hypergeometric Functions of Four Variables Sun, 15 Jun 2014 00:00:00 +0000 http://www.hindawi.com/journals/cjm/2014/273064/ In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. Here we choose the Exton function among his 21 functions to show how to find the linearly independent solutions of partial differential equations satisfied by this function . Based upon the classical derivative and integral operators, we introduce a new operational images for hypergeometric function . By means of these operational images, a number of finite series and decomposition formulas are then found. Maged G. Bin-Saad and Anvar Hasanov Copyright © 2014 Maged G. Bin-Saad and Anvar Hasanov. All rights reserved. New Čebyšev Type Inequalities and Applications for Functions of Self-Adjoint Operators on Complex Hilbert Spaces Thu, 05 Jun 2014 12:01:45 +0000 http://www.hindawi.com/journals/cjm/2014/363050/ Several new error bounds for the Čebyšev functional under various assumptions are proved. Applications for functions of self-adjoint operators on complex Hilbert spaces are provided as well. Mohammad W. Alomari Copyright © 2014 Mohammad W. Alomari. All rights reserved. Study of a Forwarding Chain in the Category of Topological Spaces between and with respect to One Point Compactification Operator Wed, 30 Apr 2014 13:52:41 +0000 http://www.hindawi.com/journals/cjm/2014/541538/ In the following text, we want to study the behavior of one point compactification operator in the chain := Metrizable, Normal, , KC, SC, US, , , , , Top of subcategories of category of topological spaces, Top (where we denote the subcategory of Top, containing all topological spaces with property , simply by ). Actually we want to know, for and , the one point compactification of topological space belongs to which elements of . Finally we find out that the chain Metrizable, , KC, SC, US, T1, , , , Top is a forwarding chain with respect to one point compactification operator. Fatemah Ayatollah Zadeh Shirazi, Meysam Miralaei, and Fariba Zeinal Zadeh Farhadi Copyright © 2014 Fatemah Ayatollah Zadeh Shirazi et al. All rights reserved. The Collatz Problem in the Light of an Infinite Free Semigroup Wed, 30 Apr 2014 11:07:12 +0000 http://www.hindawi.com/journals/cjm/2014/756917/ The Collatz (or ) problem is examined in terms of a free semigroup on which suitable diophantine and rational functions are defined. The elements of the semigroup, called T-words, comprise the information about the Collatz operations which relate an odd start number to an odd end number, the group operation being the concatenation of T-words. This view puts the concept of encoding vectors, first introduced in 1976 by Terras, in the proper mathematical context. A method is described which allows to determine a one-parameter family of start numbers compatible with any given T-word. The result brings to light an intimate relationship between the Collatz problem and the problem. Also, criteria for the rise or fall of a Collatz sequence are derived and the important notion of anomalous T-words is established. Furthermore, the concept of T-words is used to elucidate the question what kind of cycles—trivial, nontrivial, rational—can be found in the Collatz problem and also in the problem. Furthermore, the notion of the length of a Collatz sequence is discussed and applied to average sequences. Finally, a number of conjectures are proposed. Manfred Trümper Copyright © 2014 Manfred Trümper. All rights reserved. An Approximation of Hedberg’s Type in Sobolev Spaces with Variable Exponent and Application Tue, 29 Apr 2014 08:54:00 +0000 http://www.hindawi.com/journals/cjm/2014/549051/ The aim of this paper is to extend the usual framework of PDE with to include a large class of cases with , whose coefficient satisfies conditions (including growth conditions) which guarantee the solvability of the problem . This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and p-Laplace equation. Abdelmoujib Benkirane, Mostafa El Moumni, and Aziz Fri Copyright © 2014 Abdelmoujib Benkirane et al. All rights reserved. Some Fixed Point Theorems under Weak Semicompatibility Sun, 27 Apr 2014 12:24:55 +0000 http://www.hindawi.com/journals/cjm/2014/618965/ The aim of the present paper is to prove some fixed point theorems by using the recent notion “weak semicompatibility.” The new notion is proper generalization of semicompatibility and can be applicable on commuting and compatible maps. We used compatible and absorbing mappings to prove theorems which also include (E.A.) property. A. S. Saluja and Mukesh Kumar Jain Copyright © 2014 A. S. Saluja and Mukesh Kumar Jain. All rights reserved. On Quasi-Pseudometric Type Spaces Tue, 15 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/cjm/2014/198685/ We introduce the concept of a quasi-pseudometric type space and prove some fixed point theorems. Moreover, we connect this concept to the existing notion of quasi-cone metric space. Eniola Funmilayo Kazeem, Collins Amburo Agyingi, and Yaé Ulrich Gaba Copyright © 2014 Eniola Funmilayo Kazeem et al. All rights reserved. Inclusion Properties of New Classes of Analytic Functions Mon, 31 Mar 2014 14:06:43 +0000 http://www.hindawi.com/journals/cjm/2014/974175/ The purpose of the present paper is to introduce certain new subclasses of analytic functions defined by Srivastava-Attiya operator and study their inclusion relationships and to obtain some interesting consequences of the inclusion relations. Mohan Das, Ramesha Chendady, and Indira Kasarkod Pal Copyright © 2014 Mohan Das et al. All rights reserved. Dynamic Behaviour under Moving Distributed Masses of Nonuniform Rayleigh Beam with General Boundary Conditions Sun, 23 Mar 2014 06:14:40 +0000 http://www.hindawi.com/journals/cjm/2014/565826/ This paper investigates the flexural vibration of a finite nonuniform Rayleigh beam resting on an elastic foundation and under travelling distributed loads. For the solution of this problem, in the first instance, the generalized Galerkin method was used. The resulting Galerkin’s equations were then simplified using the modified asymptotic method of Struble. The simplified second-order ordinary differential equation was then solved using the method of integral transformation. The closed form solution obtained was analyzed and results show that, an increase in the values of foundation moduli and rotatory inertia correction factor reduces the response amplitudes of both the clamped-clamped nonuniform Rayleigh beam and the clamped-free nonuniform Rayleigh beam. Also for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for the moving distributed force problem. Hence resonance is reached earlier in the former. Furthermore, resonance conditions for the dynamical system are attained significantly by both and for the illustrative end conditions considered. Emem Ayankop Andi and Sunday Tunbosun Oni Copyright © 2014 Emem Ayankop Andi and Sunday Tunbosun Oni. All rights reserved. Generalizations of Inequalities for Differentiable Co-Ordinated Convex Functions Wed, 19 Mar 2014 09:54:17 +0000 http://www.hindawi.com/journals/cjm/2014/741291/ A generalized lemmas is proved and several new inequalities for differentiable co-ordinated convex and concave functions in two variables are obtained. Feixiang Chen Copyright © 2014 Feixiang Chen. All rights reserved. A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations Thu, 13 Mar 2014 13:38:23 +0000 http://www.hindawi.com/journals/cjm/2014/369713/ Based on Ostrowski's method, a new family of eighth-order iterative methods for solving nonlinear equations by using weight function methods is presented. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore, this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on evaluations could achieve optimal convergence order . Thus, we provide a new class which agrees with the conjecture of Kung-Traub for . Numerical comparisons are made to show the performance of the presented methods. Taher Lotfi and Tahereh Eftekhari Copyright © 2014 Taher Lotfi and Tahereh Eftekhari. All rights reserved. On Liouville Sequences in the Non-Archimedean Case Wed, 05 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/cjm/2014/813924/ We study Liouville numbers in the non-Archimedean case. We deal with the concept of a Liouville sequence in the non-Archimedean case and we give some results both in the p-adic numbers field and the functions field . Hamza Menken and Abdulkadir Aşan Copyright © 2014 Hamza Menken and Abdulkadir Aşan. All rights reserved. On the Estimation of Parameter of Weighted Sums of Exponential Distribution Tue, 04 Mar 2014 07:30:57 +0000 http://www.hindawi.com/journals/cjm/2014/241964/ The random variable , with and   being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of . The main problem is estimating the parameter that has the main state in applicable research. In this paper we show that estimating the parameter by using the relation between and mode is available. The mean square error values are obtained for estimating by mode, moment method, and maximum likelihood method. N. Abbasi, A. Namju, and N. Safari Copyright © 2014 N. Abbasi et al. All rights reserved. Growth Rates of Meromorphic Functions Focusing Relative Order Sun, 02 Mar 2014 14:00:22 +0000 http://www.hindawi.com/journals/cjm/2014/582082/ A detailed study concerning some growth rates of composite entire and meromorphic functions on the basis of their relative orders (relative lower orders) with respect to entire functions has been made in this paper. Sanjib Kumar Datta, Tanmay Biswas, and Sarmila Bhattacharyya Copyright © 2014 Sanjib Kumar Datta et al. All rights reserved. Wiener Polarity Index of Cycle-Block Graphs Thu, 27 Feb 2014 16:26:08 +0000 http://www.hindawi.com/journals/cjm/2014/476705/ The Wiener polarity index of a graph is the number of unordered pairs of vertices of such that the distance between and is 3. Cycle-block graph is a connected graph in which every block is a cycle. In this paper, we determine the maximum and minimum Wiener polarity index of cycle-block graphs and describe their extremal graphs; the extremal graphs of 4-uniform cactus with respect to Wiener polarity index are also discussed. Zhen Jia, Fuyi Wei, and Yang Wu Copyright © 2014 Zhen Jia et al. All rights reserved. Existence for a Second-Order Impulsive Neutral Stochastic Integrodifferential Equations with Nonlocal Conditions and Infinite Delay Thu, 27 Feb 2014 06:29:02 +0000 http://www.hindawi.com/journals/cjm/2014/143860/ The current paper is concerned with the existence of mild solutions for a class of second-order impulsive neutral stochastic integrodifferential equations with nonlocal conditions and infinite delays in a Hilbert space. A sufficient condition for the existence results is obtained by using the Krasnoselskii-Schaefer-type fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. Finally, an application to the stochastic nonlinear wave equation with infinite delay is given. Dang Huan Diem Copyright © 2014 Dang Huan Diem. All rights reserved. Disjointness Preserving and Functional Type Disjointness Preserving Operators Tue, 25 Feb 2014 08:55:10 +0000 http://www.hindawi.com/journals/cjm/2014/838692/ A new concept called functional type disjointness preserving operators is introduced and structure of disjointness preserving and functional type disjointness preserving operators on some function spaces are analysed. C. Ganesa Moorthy and C. T. Ramasamy Copyright © 2014 C. Ganesa Moorthy and C. T. Ramasamy. All rights reserved. Asymptotic I-Equivalence of Two Number Sequences and Asymptotic I-Regular Matrices Mon, 24 Feb 2014 14:04:22 +0000 http://www.hindawi.com/journals/cjm/2014/805857/ We study I-equivalence of the two nonnegative sequences and . Also we define asymptotic I-regular matrices and obtain conditions for a matrix to be asymptotic I-regular. Hafize Gumus, Jeff Connor, and Fatih Nuray Copyright © 2014 Hafize Gumus et al. All rights reserved. Multinorms and Approximate Amenability of Weighted Group Algebras Sun, 23 Feb 2014 06:20:32 +0000 http://www.hindawi.com/journals/cjm/2014/410262/ Let G be a locally compact group, and take with . We prove that, for any left -multiinvariant functional on and for any weight function on , the approximate amenability of the Banach algebra implies the left -amenability of , but in general the opposite is not true. Our proof uses the notion of multinorms. We also investigate the approximate amenability of . Saman Ghaderkhani Copyright © 2014 Saman Ghaderkhani. All rights reserved. Univalency and Convexity Conditions for a General Integral Operator Thu, 20 Feb 2014 09:20:54 +0000 http://www.hindawi.com/journals/cjm/2014/923984/ For analytic functions and in the open unit disc , a new general integral operator is introduced. The main objective of this paper is to obtain univalence condition and order of convexity for this general integral operator. Serap Bulut and Daniel Breaz Copyright © 2014 Serap Bulut and Daniel Breaz. All rights reserved. Common Fixed Point of (, )-Generalized Contractive Mappings in Partially Ordered Metric Spaces Wed, 19 Feb 2014 11:37:24 +0000 http://www.hindawi.com/journals/cjm/2014/379049/ Gordji et al. (2012) gave a generalization of Geraghty’s theorem. The aim of this paper is to study the necessary conditions for the existence of coincidence and common fixed point of four mappings satisfying (, )-generalized contractive condition in the setup of partial ordered metric spaces. Some examples are given to validate the definitions and results presented herein. M. Abbas, I. Zulfaqar, and Stojan Radenović Copyright © 2014 M. Abbas et al. All rights reserved. Modified Homotopy Perturbation Technique for the Approximate Solution of Nonlinear Equations Tue, 18 Feb 2014 12:52:51 +0000 http://www.hindawi.com/journals/cjm/2014/787591/ We use a new modified homotopy perturbation method to suggest and analyze some new iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations. Farooq Ahmed Shah Copyright © 2014 Farooq Ahmed Shah. All rights reserved. Fuzzy Soft System and Arrhythmia Classification Tue, 18 Feb 2014 12:48:48 +0000 http://www.hindawi.com/journals/cjm/2014/164781/ An arrhythmia is an irregularity with the speed or rhythm of the heartbeat. During an arrhythmia, the heart can beat too fast, too slow, or with an irregular rhythm. Most arrhythmias are harmless, but some can be serious or even life threatening. The present paper deals with the classification scheme of arrhythmia commonly occurring in human beings of Southeast Asian countries. Medical knowledge used in practice has been closely studied for modelling user friendly referral system to sharpen arrhythmia diagnosis by experts and this system is tested with satisfactory factor which is measured with degree of match criterion under the domain of considered inputs and computed output. Pankaj Srivastava, Neeraja Sharma, and C. S. Aparna Copyright © 2014 Pankaj Srivastava et al. All rights reserved. Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential Tue, 18 Feb 2014 00:00:00 +0000 http://www.hindawi.com/journals/cjm/2014/804383/ We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem. Yalçın Güldü and Merve Arslantaş Copyright © 2014 Yalçın Güldü and Merve Arslantaş. All rights reserved. Existence of Mild Solutions for Impulsive Fractional Stochastic Differential Inclusions with State-Dependent Delay Mon, 17 Feb 2014 16:22:20 +0000 http://www.hindawi.com/journals/cjm/2014/981714/ We study the existence of mild solutions for a class of impulsive fractional stochastic differential inclusions with state-dependent delay. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O’Regan. An example is given to illustrate the theory. Toufik Guendouzi and Ouahiba Benzatout Copyright © 2014 Toufik Guendouzi and Ouahiba Benzatout. All rights reserved. New Operational Matrix of Integrations and Coupled System of Fredholm Integral Equations Thu, 13 Feb 2014 11:34:25 +0000 http://www.hindawi.com/journals/cjm/2014/146013/ We study Legendre polynomials and develop new operational matrix of integration. Based on the operational matrix, we develop a new method to solve a coupled system of Fredholm integral equations of the form , , where , , , and are real constants and . The method reduces the coupled system to a system of easily solvable algebraic equations without discretizing the original system. As an application, we provide examples and numerical simulations demonstrating that the results obtained using the new technique match very well with the exact solutions of the problems. To show the efficiency of the method, we compare our results with some of the results already studied with other available methods in the literature. Hammad Khalil and Rahmat Ali Khan Copyright © 2014 Hammad Khalil and Rahmat Ali Khan. All rights reserved. Translation, Creation and Annihilation of Poles and Zeros with the Biernacki and Ruscheweyh Operators, Acting on Meijer's -Functions Wed, 12 Feb 2014 09:40:10 +0000 http://www.hindawi.com/journals/cjm/2014/716718/ Meijer's G-functions are studied by the Biernacki and Ruscheweyh operators. These operators are special cases of the Erdélyi-Kober operators (for ). The effect of operators on Meijer's G-functions can be shown as the change in the distribution of poles and zeros on the complex plane. These poles and zeros belong to the integrand, a ratio of gamma functions, defining the Meijer's G-function. Displacement in position and increasing or decreasing in number of poles and zeroes are expressed by the transporter, creator, and annihilator operators. With special glance, three basic univalent Meijer's G-functions, Koebe, and convex functions are considered. Amir Pishkoo and Maslina Darus Copyright © 2014 Amir Pishkoo and Maslina Darus. All rights reserved.