Chinese Journal of Mathematics
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© 2015 , Hindawi Publishing Corporation . All rights reserved.

Classical Ergodicity and Modern Portfolio Theory
Sun, 02 Aug 2015 11:35:49 +0000
http://www.hindawi.com/journals/cjm/2015/737905/
What role have theoretical methods initially developed in mathematics and physics played in the progress of financial economics? What is the relationship between financial economics and econophysics? What is the relevance of the “classical ergodicity hypothesis” to modern portfolio theory? This paper addresses these questions by reviewing the etymology and history of the classical ergodicity hypothesis in 19th century statistical mechanics. An explanation of classical ergodicity is provided that establishes a connection to the fundamental empirical problem of using nonexperimental data to verify theoretical propositions in modern portfolio theory. The role of the ergodicity assumption in the ex post/ex ante quandary confronting modern portfolio theory is also examined.
Geoffrey Poitras and John Heaney
Copyright © 2015 Geoffrey Poitras and John Heaney. All rights reserved.

On Quasimetrizability of Quasicone Metric Spaces
Thu, 09 Jul 2015 11:02:19 +0000
http://www.hindawi.com/journals/cjm/2015/392190/
The aim of this work is to extend interesting results on the metrizability of cone metric spaces as it appears in the literature. In this paper we appeal to quasiuniformities and uniformities to prove that a quasicone metric space is qausimetrizable, and from our results we will deduce that every cone metric space is metrizable; our approach is more on bitopological and topological properties and differs from the one used by the papers mentioned above but affirms some of their results.
M. Aphane and S. P. Moshokoa
Copyright © 2015 M. Aphane and S. P. Moshokoa. All rights reserved.

On the Stochastic Stability and Boundedness of Solutions for Stochastic Delay Differential Equation of the Second Order
Tue, 31 Mar 2015 13:20:06 +0000
http://www.hindawi.com/journals/cjm/2015/358936/
We present two qualitative results concerning the solutions of the following equation: ; the first result covers the stochastic asymptotic stability of the zero solution for the above equation in case , while the second one discusses the uniform stochastic boundedness of all solutions in case . Sufficient conditions for the stability and boundedness of solutions for the considered equation are obtained by constructing a Lyapunov functional. Two examples are also discussed to illustrate the efficiency of the obtained results.
A. M. A. AbouElEla, A. I. Sadek, A. M. Mahmoud, and R. O. A. Taie
Copyright © 2015 A. M. A. AbouElEla et al. All rights reserved.

On Transitive Points in a Generalized Shift Dynamical System
Mon, 05 Jan 2015 06:54:37 +0000
http://www.hindawi.com/journals/cjm/2015/519357/
Considering point transitive generalized shift dynamical system for discrete with at least two elements and infinite , we prove that is countable and has at most elements. Then, we find a transitive point of the dynamical system for with and show that point transitive , for infinite countable , is a factor of .
Bahman Taherkhani and Fatemah Ayatollah Zadeh Shirazi
Copyright © 2015 Bahman Taherkhani and Fatemah Ayatollah Zadeh Shirazi. All rights reserved.

On Some Integral Inequalities Related to HermiteHadamardFejér Inequalities for Coordinated Convex Functions
Mon, 17 Nov 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/796132/
Several new mappings associated with coordinated convexity are proposed, by which we obtain some new HermiteHadamardFejér type inequalities for coordinated convex functions. We conclude that the results obtained in this work are the generalizations of the earlier results.
Ruiyin Xiang and Feixiang Chen
Copyright © 2014 Ruiyin Xiang and Feixiang Chen. All rights reserved.

Differential Subordination with Generalized Derivative Operator of Analytic Functions
Wed, 20 Aug 2014 10:48:28 +0000
http://www.hindawi.com/journals/cjm/2014/656258/
Motivated by generalized derivative operator defined by the authors (ElYagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given.
Entisar ElYagubi and Maslina Darus
Copyright © 2014 Entisar ElYagubi and Maslina Darus. 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 FourthOrder 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 fourthorder 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 HermiteHadamard Type Inequalities for RiemannLiouville 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 HermiteHadamard type inequalities for products of two convex functions via RiemannLiouville 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 boundaryvalue 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. BinSaad and Anvar Hasanov
Copyright © 2014 Maged G. BinSaad and Anvar Hasanov. All rights reserved.

New Čebyšev Type Inequalities and Applications for Functions of SelfAdjoint 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 selfadjoint 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 Twords, 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 Twords. 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 oneparameter family of start numbers compatible with any given Tword. 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 Twords is established. Furthermore, the concept of Twords 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 reactiondiffusion equations, Burgers type equation, NavierStokes equation, and pLaplace 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 QuasiPseudometric Type Spaces
Tue, 15 Apr 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/198685/
We introduce the concept of a quasipseudometric type space and prove some fixed point theorems. Moreover, we connect this concept to the existing notion of quasicone 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 SrivastavaAttiya 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 secondorder 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 clampedclamped nonuniform Rayleigh beam and the clampedfree 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 CoOrdinated 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 coordinated convex and concave functions in two variables are obtained.
Feixiang Chen
Copyright © 2014 Feixiang Chen. All rights reserved.

A New Optimal EighthOrder OstrowskiType 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 eighthorder 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 KungTraub 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 NonArchimedean Case
Wed, 05 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/cjm/2014/813924/
We study Liouville numbers in the nonArchimedean case. We deal with the concept of a Liouville sequence in the nonArchimedean case and we give some results both in the padic 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 CycleBlock 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. Cycleblock 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 cycleblock graphs and describe their extremal graphs; the extremal graphs of 4uniform 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 SecondOrder 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 secondorder 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 KrasnoselskiiSchaefertype 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 IEquivalence of Two Number Sequences and Asymptotic IRegular Matrices
Mon, 24 Feb 2014 14:04:22 +0000
http://www.hindawi.com/journals/cjm/2014/805857/
We study Iequivalence of the two nonnegative sequences and . Also we define asymptotic Iregular matrices and obtain conditions for a matrix to be asymptotic Iregular.
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.