International Journal Of Nonlinear Analysis And Applications
Volume:2 Issue: 1, Summer - Autumn 2011

We describe a variational problem on a surface under a constraint of geometrical character. Necessary and sufficient conditions for the existence of bifurcation points are provided. In local coordinates the problem corresponds to a quasilinear elliptic boundary value problem. The problem can be considered as a physical model for several applications referring to continuum medium and membranes.

In this paper, we reconstruct the Hardy-Littlewood’s inequality by using the method of the weight coefficient and the technic of real analysis including a best constant factor. An open problem is raised.

In this paper, we provide a short account of the study of Hilbert-type inequalities during the past almost 100 years by introducing multi-parameters and using the method of weight coefficients. A basic theorem of Hilbert-type inequalities with the homogeneous kernel of −−degree and parameters is proved.

In this paper, we present an application of the stochastic calculus to the problem of modeling electrical networks. The filtering problem have an important role in the theory of stochastic differential equations(SDEs). In this article, we present an application of the continuous Kalman-Bucy filter for a RL circuit. The deterministic model of the circuit is replaced by a stochastic model by adding a noise term in the source. The analytic solution of the resulting stochastic integral equations are found using the Ito formula.

Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+ Fk,n−2 for n  2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functional equation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve this equation and prove its Hyere-Ulam stability in the class of functions f: N×R! X, where X is a real Banach space.

In this paper, we generalize Fuzzy Banach contraction theorem established by V. Gregori and A. Sapena [Fuzzy Sets and Systems 125 (2002) 245-252] using notion of altering distance which was initiated by Khan et al. [Bull. Austral. Math. Soc., 30(1984), 1-9] in metric spaces.

We present some new results on the existence and the approximation of common fixed point of expansive mappings and semigroups in probabilistic metric spaces.

The paper deal with non-commutative geometry. The notion of quantum spheres was introduced by podles. Here we define the quantum hermitian metric on the quantum spaces and find it for the quantum spheres.

In this paper, we introduce the concept of generalized -contractivity of a pair of maps w.r.t. another pair. We establish a common fixed point result for two pairs of self-mappings, when one of these pairs is generalized -contraction w.r.t. the other and study the well-posedness of their fixed point problem. In particular, our fixed point result extends the main result of a recent paper of Qingnian Zhang and Yisheng Song.

The main goal of this note is to introduce another second-order difference equation where every nontrivial solution is of minimal period 5, namely the difference equation: x_n+1 = 1 + x_n-1 x_nx_n-1-1, n = 1, 2, 3,. .. with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

The purpose of this paper is to study and give the necessary and sufficient condition of strong convergence of the multi-step iterative algorithm with errors for a finite family of generalized asymptotically quasi-nonexpansive mappings to converge to common fixed points in Banach spaces. Our results extend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8, 11, 14, 19]).

We consider the bilinear Fourier integral operator S(f, g)(x) = Z Rd Z Rd ei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d, on modulation spaces. Our aim is to indicate this operator is well defined on S(Rd) and shall show the relationship between the bilinear operator and BFIO on modulation spaces.