The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation

The question of interest in the present study is ”given a work-piece subject to prescribed loads, how to define its initial shape such that the work-piece matches a prescribed geometry after deformation?”. This question is particularly relevant in forming processes where the tolerated mismatch between the deformed and desired geometries may be lower than a Micron. To tackle this optimal shape d...

Abstract: In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monot...

In the present paper, the Hyers-Ulam stability and also the superstability of double centralizers and multipliers on Banach algebras are established by using a fixed point method. With this method, the condition of without order on Banach algebras is no longer necessary.

We study observation-based strategies for two-player turnbased games on graphs with omega-regular objectives. An observationbased strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a controller that does not see the private state of the plant. Our main results are twofold. First, we give a fixe...

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.

In this paper, the existence of a unique solution of Volterra-Hammerstein integral equation of the second kind (VHIESK) is proved by using Banach fixed point theorem (BFPT) in the space ] , 0 [ ) ( 2 T C L   , where  represents the domain of integration of the variable space and T is the time. Then, different kinds of projectioniteration methods (PIMs) for solving this integral equation in t...

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...