Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only be studied using their orbits. Therefore the standard notion of chaos is not immediately applicable. However, when a suitable definition is used, it is foun...

Th. M. Rassias 1984 proved that the norm defined over a real vector space X is induced by an inner product if and only if for a fixed integer n ≥ 2, ∑ni 1 ‖xi − 1/n ∑n j 1 xj‖ ∑n i 1 ‖xi‖ − n‖ 1/n ∑ni 1 xi‖ holds for all x1, . . . , xn ∈ X. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation ∑n i 1 f ...

In this paper, we apply a successful combination of three key tools which allows to get a measure of the cost of the approximate controllability for semilinear heat equation. The first tool consists to get enough information about the approximate control for the linear heat equation with a potential depending on space-time variable. Then a fixed point method is applied. The fixed point techniqu...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.

and Applied Analysis 3 Theorem 1.3 see 26–28 . Let X, d be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant L < 1. Then for each given element x ∈ X, either d ( Jx, J 1x ) ∞ 1.7 for all nonnegative integers n or there exists a positive integer n0 such that 1 d Jx, J 1x < ∞, for all n ≥ n0; 2 the sequence {Jnx} converges to a fixed p...

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiı̆–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed po...

* Correspondence: [email protected]. kr Department of Mathematics, Daejin University, Kyeonggi 487711, Korea Full list of author information is available at the end of the article Abstract Using fixed point method, we investigate the Hyers-Ulam stability and the superstability of partial generalized Jordan derivations on Banach modules related to Jensen type functional equations. Mathematics Subj...

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed poin...

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.