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.
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 a nonempty closed convex subset of X, hn, where a sequence of contractions on C and Tn , for a nite family of commuting nonexpansive mappings on C. We show that under appropriate conditions on the explicit iterative sequence dened by
where converges strongly to a common xed point We consequently show that the results is true for an innite family of commuting nonexpansive mapping on C
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.
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.