Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, θ an involution of G defined over k, H a k-open subgroup of the fixed point group of θ and Gk (resp. Hk) the set of k-rational points of G (resp. H). The variety Gk/Hk is called a symmetric k-variety. For real and -adic symmetric k-varieties the space L(Gk/Hk ) of square integrable functions decompose...

In this paper, we propose a three-step iteration scheme for nonself asymptotically nonexpansive type mappings in a complete CAT(0) metric space and establish necessary and sufficient conditions for convergence of this process to a fixed point of nonself asymptotically nonexpansive type mappings. We also establish a strong convergence result. These results generalize and unify many important res...

In this paper,we establish fixed points theorems in Banach space using Mann Iteration for nonexpansive and asymtotically nonexpansive mappings . Iteration scheme is defined by (2.1) and (2.2). We extended the work of Mann.

Using inverse positivity properties and Brouwer’s fixed point theorem, we derive existence and uniqueness results for certain nonlinear systems of equations with off diagonal nonlinearity. The type of systems considered arises from stable finite volume discretizations of viscous nonlinear conservation laws and has a wide range of applications.

In the present note, it is proved that if a random Mann iteration scheme defined by two operators is convergent under some contractive inequality the limit point is a common fixed point of each of two random operators in a Banach space.

We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition cont...

Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.

where t ∈ T = [ν – β – 1,b + ν – β – 1]Nν–β–1 . βν–2, b∇ν are left and right fractional difference operators, respectively, and φp(s) = |s|p–2s, p > 1. By using the method of upper and lower solution and the Schauder fixed point theorem, we obtain the existence of positive solutions for the above boundary value problem; and applying a monotone iterative technique, we establish iterative schemes...