论文标题
通过连续近似和贝尔多项式的变形广义斐波那契多项式的功能差异方程的解决方案的存在
Existence of Solutions of Functional-Difference Equations with Proportional Delay on Deformed Generalized Fibonacci Polynomials via Successive Approximation and Bell Polynomials
论文作者
论文摘要
在本文中，我们研究了通过连续近似方法和贝尔多项式对变形的斐波那契多项式的功能差方程的解决方案的存在。首先，我们介绍了变形的概括性斐波那契多项式，并表明$ q $ numbers可以看作是变形$（s，t）$ - 数字的“分叉”。这些变形与比例延迟密切相关。其次，引入了变形的斐波那契多项式上的差分和积分积分。引入该计算的主要原因是要有一个框架来求解比例功能方程，从而获得了pell cyculus，jacobsthal colculus，chebysheff colculus和Mersenne Colculus等。我们研究$（s，t）$ - 指数类型系列的收敛性及其对变形参数的依赖性。我们定义了变形的$（s，t）$ - 指数函数，并提供其分析和代数属性。此外，我们研究了$（1，u）$ - 变形$（s，t）$ - 指数函数，并使用它来证明存在具有比例延迟的功能差方程。当解决方案与$ Q $ - 周期功能相关时，该解决方案并不是唯一的。
In this paper, we study the existence of solutions of the functional difference equations with proportional delay on deformed generalized Fibonacci polynomials via successive approximation method and Bell polynomials. First, we introduce the deformed generalized Fibonacci polynomials and show that the $q$-numbers can be viewed as "bifurcation" of deformed $(s,t)$-numbers. These deformations are closely related to proportional delay. Second, a differential and integral calculus on deformed generalized Fibonacci polynomials is introduced. The main reason for introducing this calculation is to have a framework for solving proportional functional equations and thus obtain the Pell calculus, Jacobsthal calculus, Chebysheff calculus, and Mersenne calculus, among others. We study the convergence of $(s,t)$-exponential type series and its dependence on the deformation parameter. We define the deformed $(s,t)$-exponential functions and we give its analytic and algebraic properties. In addition, we study the $(1,u)$-deformed $(s,t)$-exponential function and use it to prove the existence of functional difference equations with proportional delay. The solution is not unique when it is related to $q$-periodic functions.
