Turkish Journal of Analysis and Number Theory

4

Authors: T. Satyanarayana, K. L. Sai Prasad

In this paper we study some remarkable properties of para Kenmotsu (briefly p-Kenmotsu) manifolds satisfying the conditions R(X,Y).R=0, R(X,Y).P=0 and P(X,Y).R=0, where R(X, Y) is the Riemannian curvature tensor and P(X, Y) is the Weyl projective curvature tensor of the manifold. It is shown that a semi-symmetric p-Kenmotsu manifold (Mn, g) is of constant curvature and hence is an sp-Kenmotsu manifold. Also, we obtain the necessary and sufficient condition for a p-Kenmotsu manifold to be Weyl projective semi-symmetric and shown that the Weyl projective semi-symmetric p-Kenmotsu manifold is projectively flat. Finally we prove that if the condition P(X,Y).R=0 is satisfied on a p-Kenmotsu manifold then its scalar curvature is constant.

2

Authors: Kunle Adegoke, Olawanle Layeni, Rauf Giwa, Gbenga Olunloyo

In this paper we give a Casimir Invariant for the Symmetric group Sn. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of the permutation representation.

6

Authors: Waseem A. Khan, N. U. Khan, Sarvat Zia

In the paper, we introduce a new concept of poly-Bernoulli numbers and polynomials of the second kind which is called Hermite poly-Bernoulli numbers and polynomials of the second kind. We also investigate and analyse its applications in number theory, combinatorics and other fields of mathematics. The results derived here are a generalization of some known summation formulae earlier studied by Jolany et al. [17,18], Dattoli et al [14] and Pathan et al [29,30].

3

Authors: K. L. Sai Prasad, T. Satyanarayana

The object of the present paper is to study some properties of curvature tensor of a semi-symmetric non-metric connection in a type of special paracontact Kenmotsu (briefly SP-Kenmotsu) manifold. We have deduced the expressions for curvature tensor and the Ricci tensor of Mn with respect to semi-symmetric non-metric connection . It is proved that in an SP-Kenmotsu manifold if the curvature tensor of the semi-symmetric non-metric connection vanishes then the manifold is projectively flat.

4

Authors: Cheon Seoung Ryoo

In [7], Ryoo introduced the generalized tangent numbers and polynomials. In this paper, our goal is to give generating functions of the degenerate generalized tangent numbers and polynomials. We also obtain some explicit formulas for degenerate generalized tangent numbers and polynomials.

7

Authors: Idir Sadani

We study the properties of prime number sequences obtained using a well-defined equivalence relation . It will be seen that the elements of each class of are all prime numbers which constitute the fundamental object of our study. The number of prime numbers of each class less than or equal to a given quantity , the number of the different equivalence classes and some other results will be deduced.

3

Authors: Vijay Sookdeo

For a Lattès map defined over a number field K, we prove a conjecture on the integrality of points in the backward orbit of under

4

Authors: S. Sivasubramanian, P. Gurusamy

In an article of Pommerenke [10] he remarked that, for an -fold symmetric functions in the class , the well known lemma stated by Caratheodary for a one fold symmetric functions in still holds good. Exploiting this concept, we introduce certain new subclasses of the bi-univalent function class in which both and are -fold symmetric analytic with their derivatives in the class of analytic functions. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for and We remark here that the concept of -fold symmetric bi-univalent is not in the literature and the authors hope it will make the researchers interested in these type of investigations in the forseeable future. By the working procedure and the difficulty involved in these procedures, one can clearly conclude that there lies an unpredictability in finding the coefficients of a -fold symmetric bi-univalent functions.

5

Authors: Amit Kumar Govery, Mamta Singh

In this paper, the concept of compatible maps of type (A) and occasionally weakly compatible maps in fuzzy metric space have been applied to prove common fixed point theorem. A fixed point theorem for six self maps has been established using the concept of compatible maps of type (A) and occasionally weakly compatible maps, which generalizes the result of Cho .

2

Authors: Azizul Hoque, Himashree Kalita

In this paper we introduce two new Arithmetic functions, that is, Quasi-Multiplicative (QM) and omega functions. The Omega function is based on Euler’s Phi function and is used to find the sum of coprime integers. Euler’s Phi function, Dedekind’s psi function, the sigma function and -function play significant role in this work.

5

Authors: Krishna Patel, G M Deheri

Results dealing with a Fixed Point for a map need not be continuous on a metric space, which improves a famous classical result, has been presented here, wherein the convergence aspect is duly addressed. This paper aims to present some fixed point theorems on metric spaces. It can be easily observed that these are significant improvement of some of the well-known classical result dealing with the generalization of Banach fixed point theorem. Further, here the rate of convergence aspects is duly taken care of.

6

Authors: Tian-Yu Zhang, Bai-Ni Guo

In the paper, by establishing two integral identities and Hölder integral inequality, the authors generalize some integral inequalities of Hermite-Hadamard type for n-time differentiable functions on a closed interval.

8

Authors: Reza Arab

In this paper, we present some coincidence and common fixed point results for infinite families of contractive maps satisfying a new class of pairs of generalized contractive type mappings defined in partial metric spaces. Our results extend and generalize many known results in the literature. Also, we introduce an example to support the validity of our results.