Turkish Journal of Analysis and Number Theory

3

Authors: Manvendra Tamba

Let G(n) denote the number of partitions of n into distinct parts which are of the form 2m, 3m, 5m, 6m-3, 8m-3, 9m-3 or 11m-3 with parts of the form 2m, 3m, 6m-3, or 11m-3 being even in number minus the number of them with parts of the form 2m, 3m, 6m-3, or 11m-3 being odd in number. In this paper, we prove that G(n) assumes all integral values and does so infinitely often.

3

Authors: Sanying Shi

Suppose that E is an algebraic number field over the rational field Let a(n) be the number of integral ideals in E with norm n and Δ(x) denote the remainder term in the asymptotic formula of the l-th integral power sum of a(n). In this paper the bound of the average behavior of Δ(x) is given. This result constitutes an improvement upon that of Lü and Wang for the error terms in mean value.

4

Authors: Kwara Nantomah

This paper presents some inequalities concerning certain ratios of the classical Euler’s Gamma function. The results generalized some recent results.

6

Authors: ERHAN SET, MUHARREM TOMAR, SELAHATTIN MADEN

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

10

Authors: Ranjit Biswas

In this paper the author introduces a new kind of numbers called by ‘Compound Numbers’. A region R may or may not have imaginary object. A region even may have more than one imaginary objects too. Corresponding to an imaginary object (if exists) of a region R, we get compound objects for the region R. Imaginary objects and compound objects of a region R are not members of R and so they are called imaginary with respect to the region R only (i.e. it is a local characteristics property with respect to the region concerned), as they could be core members of another region. Every region has its own set of imaginary numbers (if exist). As a particular instance, the compound objects of the set of real numbers are the complex numbers (of existing concept). In this paper the author discovers imaginary objects of the region C (the set of complex numbers). The compound objects of C are called by ‘compound numbers’. Collection of all compound numbers is denoted by the set E. This work just reports the birth of compound numbers, not further details at this stage. It is claimed that “Theory of Numbers” will get a new direction by the birth of compound numbers. A new “Theory of Objects’ and the classical “Theory of Numbers” as a special case of it were also studied in [16]. In this paper we say that every complete region has its own ‘Theory of Numbers’, where the classical ‘theory of numbers’ is just a special instance corresponding to a particular complete region RR. Consequently, we also introduce a new field called by “Object Geometry” of a complete region, being a generalization of our classical geometry of the existing style, from elementary to the higher level.

4

Authors: Omprakash Sikhwal, Yashwant Vyas

The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, some determinant identities of Fibonacci polynomials are describe. Entries of determinants are satisfying the recurrence relations of Fibonacci polynomials and Lucas polynomials.

6

Authors: Mamta Singh, Omprakash Sikhwal, Yogesh Kumar Gupta

The Fibonacci and Lucas sequences are well-known examples of second order recurrence sequences. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, n≥2 and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation Mn=Mn-1+Mn-2, n≥2, with M0=2, M1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence are presented by Binet’s formula. Also some determinant identities are discussed.

7

Authors: Mehmet Zeki SARIKAYA, Hüseyin BUDAK, Hatice YALDIZ

In this paper, we obtain new identity for function of two variables and apply them to give new Ostrowski type integral inequality for double integrals involving functions whose derivatives are co-ordinates convex function on in R2 with .

3

Authors: Sanjay Harne, V.H. Badshah, Sapna Sethiya

Determinants have played a significant part in various areas in mathematics. For instance, they are quite useful in the analysis and solution of system of linear equations. There are different perspectives on the study of determinant. In this paper we present some determinant identities of Fibonacci and Lucas numbers.

5

Authors: Sabuj Das, Haradhan Kumar Mohajan

This paper shows that the coefficient of x in the right hand side of the equation is an algebraic relation in terms of z. The exponent of z represents the crank of partitions of a positive integral value of n and also shows that the sum of weights of corresponding partitions of n is the sum of ordinary partitions of n and it is equal to the number of partitions of n with crank m. This paper shows how to prove the Theorem “The number of partitions π of n with crank C(π)=m is M(m,n) for all n>1.”

6

Authors: MEVLÜT TUNÇ, IBRAHİM KARABAYIR, EBRU YÜKSEL

In this paper, the authors achieve some new Hadamard type in- equalities using elementary well known inequalities for functions whose second derivatives absolute values are s-geometrically and geometrically convex. And also they get some applications for special means for positive numbers.

6

Authors: Wei-Dong Jiang, Qiu-Ming Luo, Feng Qi

In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened.

5

Authors: Tian-Yu Zhang, Feng Qi

In the paper, the authors introduce the concept “m-AH convex functions” and establish some inequalities of Hermite-Hadamard type for m-AH convex functions.

5

Authors: Ruihua Cao

In this note, a boundary integral equation method coupled with the method of fundamental solutions for solving an inverse heat conduction problem is considered. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on GCV criterion. To illustrate our main results, some numerical examples are given.

5

Authors: Mehmet Zeki SARIKAYA, Hüseyin BUDAK

The main of this paper is to establish an Ostrowski type inequality for two variables functions by using a mean value theorem.

6

Authors: Chandrashekar Adiga, M. S. Surekha, A. Vanitha

In this paper, we derive new identities involving a continued fraction of Ramanujan of order twelve that are similar to those of the Ramanujan-Göllnitz-Gordon continued fraction.

8

Authors: Aleksandar Ivić

Let denote the error term in the Dirichlet divisor problem, and the error term in the asymptotic formula for the mean square of If with then we discuss bounds for third, fourth and fifth power moment of We also prove that always changes sign in for and obtain (conditionally) the existence of its large positive, or small negative values.

5

Authors: Kastriot Zoto, Elida Hoxha, Panda Sumati Kumari

In this paper we prove some fixed point theorems for one and two pairs of selfmaps which are occasionally weakly compatible and satisfy a “max” and contractive conditions. Also, some existing results are derived as corollaries from theorems of this paper in the framework of dislocated metric spaces.

6

Authors: M.T. Yahyapour, S.A. Edalatpanah

In this paper, we present an efficient numerical method for solving the linear complementarity problems based on preconditioning strategy. Furthermore, the convergence properties of the proposed method have been analyzed and compared with symmetric successive over-relaxation (SSOR) method. Finally, some numerical experiments are illustrated to show the efficiency of the proposed method.

8

Authors: Roberto B. Corcino, Harren Jaylo-Campos, Amila P. Macodi-Ringia

The noncentral Stirling numbers of the first and second kind are certain generalization of the classical Stirling numbers of both kinds. In this paper, a kind of generalized Bell numbers, called noncentral Bell numbers, are defined in terms of noncentral Stirling numbers of the second kind. Some properties parallel to the ordinary Bell numbers are established including the Hankel transform of noncentral Bell numbers. Moreover, an alternative proof for the Hankel transform of (r, β)-Bell numbers is presented.