In this paper, we introduce a way of representing given mapping as the sum odd and even mappings. Then, using representation, investigate stability various forms following general nonic functional equation: ∑i=01010Ci(−1)10−if(x+iy)=0.

Abstract We prove the Hyers–Ulam stability of functional equation $$\begin{aligned}&f(a_1x_1+a_2x_2,b_1y_1+b_2y_2)=C_{1}f(x_1,y_1)\nonumber \\ \nonumber \\&\quad +C_{2}f(x_1,y_2)+C_{3}f(x_2,y_1)+C_{4}f(x_2,y_2) \end{aligned}$$ f ( ...

We consider the kinetic Fokker–Planck equation with a class of general force. prove existence and uniqueness positive normalized equilibrium (in case force) establish some exponential rate convergence to (and can be explicitly computed). Our results improve about classical force case. result also improves for Fitzhugh–Nagumo from non-quantitative quantitative explicit rate.

A general game player is an agent capable of taking as input a description of a game’s rules in a formal language and proceeding to play without any subsequent human input. To do well, an agent should learn from experience with past games and transfer the learned knowledge to new problems. We introduce a graph-based method for identifying previously encountered games and prove its robustness fo...