in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

This article introduces a new family of Generalized Exponentiated Exponential distribution. Using the T-R{Y} framework, T-Exponentiated Exponential{Y} distributions named Exponential{Frechet} is proposed. Some general properties such as hazard rate function, quantile non-central moment, mode, mean absolute deviations and Shannon’s entropy are discussed. A continuous univariate probability distr...

Let X be a real or complex Banach space and Y be a normed linear space. Suppose that f:X → Y is a Frechet differentiable function and F:X ⇉ 2 is a set-valued mapping with closed graph. Uniform convergence of Chord method for solving generalized equation y ∈ f x + F x ...... . (∗), where y ∈ Y a parameter, is studied in the present paper. More clearly, we obtain the uniform convergence of the se...

(Thus the subgradients of / correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E®R lying above the graph of /.) The set of subgradients of / at x is denoted by dfix). If d/(x) is not empty, / is said to be subdifferentiable at x. If/actually had a gradient x* = V/(x) at x in the sense of Gateaux (or Frechet), one would in particular have d/(x)...

We prove some general results on sequential convergence in Frechet lattices that yield, as particular instances, the following regarding a closed ideal \(I\) of Banach lattice \(E\): (i) If two \(E\), and \(E/I\) have positive Schur property (the property, respectively) then third has well; (ii) dual \(E\) also this property; (iii) weak Dunford-Pettis property. Examples applications are provided.

1. Introduction While aerodynamic prediction methods based CFD are now well established , and quite accurate and robust, the ultimate need in the design process is to find the optimum shape which maximizes the aerodynamic performance. One way to approach this objective is to view it as a control problem, in which the wing is treated as a device which controls the flow to produce lift with minim...