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Journal of Analysis & Number Theory
An International Journal



Error Bernoulli Polynomials and their Relations to Hermite Polynomials

Hunduma Legesse Geleta,
Abstract :
In this article we introduce and investigate new families of polynomials Bn( 1/2 ; x) called error Bernoulli polynomials through generating functions, Appell sequences andUmbral Calculus. We also show that these polynomials are related to the Hermite polynomials.


m-Normal Cone Metric Spaces

Mohammed Shehu Shagari,
Abstract :
In this paper, by using the concept of Archimedean property, m-normal cone metric space is introduced and some fixed point theorems of contractive mappings satisfying weak contractive conditions on m-normal cone metric space are proved. An example illustrating this concept is given.


Fixed Points of Non-self Mappings in Partial Metric Spaces

Santosh Kumar, Terentius Rugumisa,
Abstract :
A number of theorems on contractive mappings for common fixed points in partial metric spaces have been proved and many of them apply to self maps. In this paper, we extend a common fixed point theorem on a partial metric space by Karapinar et al. so that it can apply to a non-self mapping in a metrically convex partial metric space under specified conditions.


Some fixed point theorems for two hybrid pairs of mappings in partial metric spaces

Santosh Kumar and Johnson Kessy,
Abstract :
In this paper some common fi xed point results for two hybrid pairs of non-self mappings in the framework of partial metric spaces are established. The main result, in particular, generalizes the metric fi xed point results due to Khan and Imdad, Ciric and Ume, and Rhoades to partial metric spaces.


Solutions for certain classes of Non-linear Diophantine Eqautions

Abstract :
ABSTRACT: The main aim of this paper is to introduce a method, to solve certain class of non-Linear Diophantine equations and investigate various properties using the well-known Eulerís theorem and the theory of congruence. Some of the interesting special cases of our main results have been discussed. KEY WORDS: Diophantine Equations, Non-linear Diophantine equations, Euler phi-function, Eulerís theorem.


Two Dimensional Laplace Transforms for Solving Systems of Fractional Partial Differential Equations

M.R. Masomi,
Abstract :
Abstract In this work, the authors implemented two dimensional Laplace transform to solve certain in homogenous sub ballistic fractional PDE and homogeneous systems of time fractional heat equations which is a generalization to the problem of thermal effects on fluid flow and also the problem of the effect of a uniform overburden on the passage of a thermal wave and the temperatures in the underlying rock. Constructive examples are also provided.

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