Idham Arif Alias

Ulam Stability of a Quartic Functional Equation

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥

On the Stability of Quadratic Double Centralizers and Quadratic Multipliers: A Fixed Point Approach

We prove the superstability of quadratic double centralizers and of quadratic multipliers on Banach algebras by fixed point methods. These results show that we can remove the conditions of being weakly commutative and weakly without order which are used in the work of M. E. Gordji et al. (2011) for Banach algebras.

Approximately cubic functional equations and cubic multipliers

In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic multipliers are superstable under some conditions.2000 Mathematics Subject Classification: 39B82; 39B52.

Approximate ternary quadratic derivations on ternary Banach algebras and C*-ternary rings

In the current article, we use a fixed point alternative theorem to establish the Hyers-Ulam stability and also the superstability of a ternary quadratic derivation on ternary Banach algebras and C*-ternary rings which is introduced in Shagholi et al.2010 Mathematics Subject Classification: 39B82; 39B52; 46H25.

Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space

We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

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Simple Motion Evasion Differential Game of One Pursuer and One Evader

ℓ2. Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed.

A Pursuit Problem Described by Infinite System of Differential Equations with Coordinate-Wise Integral Constraints on Control Functions

The approach of a group of controlled objects, the pursuers, to another one, the evaders, is considered. The motions of all the objects are described by simple differential equations. The control functions of players are subjected to integral constraints. The amount of control resources such as fuel, energy etc. are described by such constraints. Given a non-empty convex subset of