Open Access Original Research Article

Existence and Uniqueness of Positive Almost Periodic Solutions for a Class of Impulsive Lotka-Volterra Cooperation Models with Delays

Chunhua Feng

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2017/29723

This paper discusses an almost periodic Lotka-Volterra cooperation system with time delays and impulsive e ects. By constructing a suitable Lyapunov functional, a sucient condition which guarantees the existence, uniqueness and uniformly asymptotically stable of almost periodic solution of this system is obtained. A new result has been provided. A suitable example indicates the feasibility of the criterion.

Open Access Original Research Article

Viscosity Approximation Methods in Reflexive Banach Spaces

K. Piesie Frimpong, E. Prempeh

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2017/33396

In this paper, we study viscosity approximation methods in re exive Banach spaces. Let X
be a re exive Banach space which admits a weakly sequentially continuous duality mapping QQ.PNG a nonempty closed convex subset of X, hn, where 111.PNG a sequence of contractions
on C and Tn , TT.PNG for YY.PNG a nite family of commuting nonexpansive mappings
on C. We show that under appropriate conditions on OO.PNG the explicit iterative sequence XXX.PNG dened
by  

 

                 SS1.PNG

 

where XXX2.PNG converges strongly to a common xed point OOO.PNG We consequently show
that the results is true for an innite family UUU.PNG of commuting nonexpansive
mapping on C

 

Open Access Original Research Article

Graceful Labelling for Complete Bipartite Fuzzy Graphs

R. Jebesty Shajila, S. Vimala

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2017/32242

The concept of fuzzy graceful labelling is introduced. A graph which admits a fuzzy graceful labelling is called a fuzzy graceful graph. Fuzzy graceful labelled graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. In this paper the concept of fuzzy graceful labelling is applied to complete bipartite graphs. Also we discussed the edge and vertex gracefulness of some complete bipartite graphs.

Open Access Original Research Article

Open Access Original Research Article

On the Notes of Quasi-Boundary Value Method for Solving Cauchy-Dirichlet Problem of the Helmholtz Equation

Benedict Barnes, F. O. Boateng, S. K. Amponsah, E. Osei-Frimpong

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2017/32727

The Cauchy-Dirichlet problem of the Helmholtz equation yields unstable solution, which when solved with the Quasi-Boundary Value Method (Q-BVM) for a regularization parameter α = 0. At this point of regularization parameter, the solution of the Helmholtz equation with both Cauchy and Dirichlet boundary conditions is unstable when solved with the Q-BVM. Thus, the quasi-boundary value method is insufficient and inefficient for regularizing ill-posed Helmholtz equation with both Cauchy and Dirichlet boundary conditions. In this paper, we introduce an expression 1/(1+α2) ; α ∈ R, where α is the regularization parameter, which is multiplied by w(x; 1) and then added to the Cauchy and Dirichlet boundary conditions of the Helmholtz equation. This regularization parameter overcomes the shortcomings in the Q-BVM to account for the stability at α = 0 and extend it to the rest of values of R.