By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

The static response of an electrostatic micro-catilever beam has been obtained by using Galerkin’s method. To make the system bi-stable, a controller has been added and the static response profile is presented using a multi-mode model for the beam. The number of mode shapes leading to convergence has been studied. The softening effect of adding more mode shapes has been investigated along with ...

We consider a Riemannian manifold (M, g) and a codimension one distribution ∆ ⊂ TM on M which is the orthogonal of a unit vector field Y onM. We do not make any nonintegrability assumption on ∆. The aim of the paper is to develop a Morse Theory for the sub-Riemannian action functional E on the space of horizontal curves, i.e. everywhere tangent to the distribution ∆. We consider the case of hor...

In this paper, we study multi-step random iteration scheme with errors for a common random fixed point of a finite family of nonself asymptotically nonexpansive random mappings in real uniformly convex separable Banach spaces. The results presented in this paper extend the recent ones announced by Zhou and Wang [23] and many others. 2000 Mathematics Subject Ciassification No.: 47H09, 47H10.

Let H be a real Hilbert space. Consider on H a nonexpansive family T = {T(t) : 0 ≤ t < ∞} with a common fixed point, a contraction f with the coefficient 0 0. Assume that 0 < γ < γ̄ /α and that S = {S (t) : 0 ≤ t < ∞} is a family of nonexpansive self-mappings on H such that F(T ) ⊆ F(S) and T has prop...

Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., `p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z0 ∈ K, zn+1 = (1 − μn+1)ω + μn+1yn; yn = (1 − αn)zn + αnTzn, converges strongly to a fixed poi...

In this paper, we prove the existence of a random common fixed point of two continuous contractive random operators on a separable Banach space. We introduce the random modified Ishikawa iteration scheme and use our existence result to study weak and strong convergence of this scheme to a unique random common fixed point of two random asymptotically quasi-nonexpansive operator. Our work extends...

We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive oper...

We provide an iterative method for finding a common solution of a finite family of equilibrium problems and of a fixed point problem, and prove its strong convergence. Our method extends an implicit method of Colao, et al. (Nonlinear Anal. 71 (2009), no. 7-8, 2708-2715) to an explicit method (in the case of a single nonexpansive mapping).