Showing papers in "Journal of Mathematical Analysis and Applications in 2007"

TL;DR: In this paper, the authors introduce cone metric spaces and prove fixed point theorems of contractive mappings on these spaces, and prove some fixed point properties of the mappings.

TL;DR: In this article, a generalized Gronwall inequality with singularity was used to study the dependence of the solution of a fractional differential equation on the order and the initial condition of the equation.

TL;DR: In this paper, a general theorem on conservation laws for arbitrary differential equations is proved, where the adjoint equation inherits all symmetries of the original equation and the conservation law does not require the existence of a Lagrangian.

TL;DR: Combettes and Hirstoaga as mentioned in this paper introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the fixed points of a nonexpansive mapping in a Hilbert space.

TL;DR: In this paper, the stability of equilibrium points in the fractional-order predator-prey model and fractionalorder rabies model is studied and the existence and uniqueness of solutions are proved.

TL;DR: Nakajo and Takahashi as mentioned in this paper showed that strong convergence for nonexpansive mappings to strict pseudo-contractions can be obtained by modifying Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence.

TL;DR: In this article, a class of h-convex functions, which generalize convex, s-concave, Godunova-Levin functions and P-functions, is introduced.

TL;DR: In this paper, the initial value problem for a class of fractional differential equations is discussed and the theoretical result established in the paper ensures the validity of chaos control of fractionial differential equations.

TL;DR: In this paper, Luo et al. showed that a sufficient large white noise may make the underlying population extinct while for a relatively small white noise, the average in time of the population is bounded.

TL;DR: In this article, a generalization of the exponential function exp ( z ) was introduced and its properties including usual differentiation and integration, Laplace transforms, Euler (Beta) transforms, Mellin transforms, Whittaker transforms, generalised hypergeometric series form and Mellin-Barnes integral representation with their several special cases are obtained and its relationship with Laguerre polynomials, Fox H-function and Wright hypergeometry function is also established.

TL;DR: In this paper, the concept of Euler-Lagrange fractional extremal was used to prove a Noether-type theorem for the calculus of variations with fractional derivatives.

TL;DR: In this article, the concept of graph energy was introduced by Gutman and Koolen and Moulton, and it was shown that Wigner's semicircle law implies that E(G ) = ( 4 3 π + o ( 1 ) ) n 3 / 2 for almost all graphs G.

TL;DR: In this paper, the authors generalized the bidirectional associative memory (BAM) model with discrete time delays in the leakage (or forgetting) terms and derived two sets of delay dependent sufficient conditions for the existence of a unique equilibrium and its asymptotic and exponential stability.

TL;DR: It is shown that the coefficients of that monic polynomial are invariants of that tensor, i.e., they are invariant under co-ordinate system changes.

TL;DR: In this paper, an epidemic model in a patchy environment with periodic coefficients is investigated, and the conditions under which the positive periodic solution is globally asymptotically stable.

TL;DR: In this paper, the multiple-sets split feasibility problem is cast into an equivalent problem in a suitable product space and a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case is presented.

TL;DR: In this article, a quadratic bound on the rate of asymptotic regularity for the Krasnoselski-Mann iterations of nonexpansive mappings in CAT(0)-spaces was obtained.

TL;DR: In this article, the dependence of (m 1, m 2 ) -convexity on m 1 and m 2 was studied and sufficient conditions for ( m 1, m 2 ), where m 1 is defined by the Maclaurin coefficients, were given.

TL;DR: In this article, the existence, uniqueness and stability of the positive steady solution for the nonlocal evolution equation under general conditions were investigated and the global dynamics were also investigated and a trichotomy of the global asymptotics was established.

TL;DR: In this paper, the authors considered the classical mathematical model with saturation response of the infection rate and obtained sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state.

TL;DR: In this paper, the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved, and the Hamilton's equations of motion are obtained in a similar manner to the usual mechanics.

TL;DR: In this article, the authors introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation, which has been used in the past for population dynamics.

TL;DR: Kim et al. as mentioned in this paper gave a new construction of q-Euler numbers, which are different from Carlitz's q-extension and author's qextension in previous publication.

TL;DR: The aim of this work is to obtain scalar representations of set-valued optimization problems without any convexity assumption by means of nonlinear scalarization, and gives two existence theorems for set- valued optimization problems.

TL;DR: In this paper, a method is presented to obtain the analytical and approximate solutions of linear and nonlinear systems of second order boundary value problems, where the analytical solution is represented in the form of series in the reproducing kernel space.

TL;DR: In this paper, a sub-supersolution principle for Dirichlet problems involving the p ( x ) -Laplacian is established, and it is proved that the local minimizers in the C 1 topology are also local minimisers in the W 1, p (x ) topology for given energy functionals.

TL;DR: The fixed point theory of set-valued contractions was developed in different directions by many authors, in particular, by [S.B. Nadler as discussed by the authors, who introduced the concept of contraction for setvalued maps in metric spaces and the conditions guaranteeing the existence of a fixed point for such a contraction are established.

TL;DR: In this article, partial neutral functional differential equations of first and second order with impulses are considered. But the results of existence of mild solutions for these classes of equations are not known.

TL;DR: In this article, implicit and explicit viscosity-like methods for finding specific common fixed points of infinite countable families of nonexpansive self-mappings in Hilbert spaces are proposed.

TL;DR: In this article, the existence theorems for a nonlinear periodic boundary value problem of first-order differential equations with impulses with impulses were proved by using Schaeffer's theorem.