We use a fixed point method to prove the Cauchy–Rassias stability of homomorphisms associated to the Pexiderized Cauchy–Jensen type functional equation r f ( x+ y r ) + sg ( x− y s ) = 2h(x), r,s ∈ R\{0}

A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

After proving a multi-dimensional extension of Zalcman’s renormalization lemma and considering maximality problems about dimensions, we find renormalizing polynomial families for iterated elementary mappings, extending this result to some kinds of correspondences (by means of ’algebraic’ renormalizing families) and to the family of the iterated mappings of an automorphism of C2 admitting a repu...

A neutral fixed point of a real iteration map u becomes a super attracting fixed point using a suitable double newtonisation. The map u is so transformed into a map w which is here called the standard accelerator of u. The map w provides a unifying process to deal with a large set of fixed point sequences which are not convergent or converge slowly. Several examples illustrate the main results ...

Let ∆ be a ball in the complex vector space C centered at the origin, let f : ∆ → C be a holomorphic mapping, with f(0) = 0, and let M be a positive integer. If the origin 0 is an isolated fixed point of the M th iteration f of f, then one can define the number OM (f, 0) of periodic orbits of f with period M hidden at the fixed point 0, which has the meaning: any holomorphic mapping g : ∆ → C s...

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.

In this paper it is shown that the intuitionistic fixed point theory ÎD i α(strict) for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and Π2 sentences over the theory ACA−i α for α times iterated arithmetic comprehension without set parameters. This generalizes results previously due to Buchholz [5] and Arai [2].

We introduce a new technique for proving the classical Stable Manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.

The purpose of this paper is to prove that the modified Mann iteration process can be applied to approximate the common fixed point of three strictly hemicontractive mappings in smooth Banach spaces.