253 research outputs found
An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics
We present a three-point iterative method without memory for solving
nonlinear equations in one variable. The proposed method provides convergence
order eight with four function evaluations per iteration. Hence, it possesses a
very high computational efficiency and supports Kung and Traub's conjecture.
The construction, the convergence analysis, and the numerical implementation of
the method will be presented. Using several test problems, the proposed method
will be compared with existing methods of convergence order eight concerning
accuracy and basin of attraction. Furthermore, some measures are used to judge
methods with respect to their performance in finding the basin of attraction.Comment: arXiv admin note: substantial text overlap with arXiv:1508.0174
Pursuit-evasion differential game with many inertial players
We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players
Some results in probabilistic n-Banach spaces
In this article, after introducing the probabilistic n-normed spaces we define probabilistic n-Banach spaces and study convergence in these spaces by some theorems
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