Related papers: On the Recurrence Formula for Fixed Points of the …
Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…
We reformulate the $3x+1$ conjecture by restricting attention to numbers congruent to $2$ (mod $3$). This leads to an equivalent conjecture for positive integers that reveals new aspects of the dynamics of the $3x+1$ problem. Advantages…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
In this article, we introduce a recurrence formula which only involves two adjacent values of the Riemann zeta function at integer arguments. Based on the formula, an algorithm to evaluate $\zeta$-values(i.e. the values of Riemann zeta…
Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval. Fixed point analysis shows that the DRS iterated…
In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.
In this paper we present some fixed-figure theorems as a geometric approach to the fixed-point theory when the number of fixed points of a self-mapping is more than one. To do this, we modify the Jleli-Samet type contraction and define new…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
This paper describes a systematic method of numerically computing and indexing fixed points of $z^{z^w}$ for fixed $z$ or equivalently, the roots of $T_2(w;z)=w-z^{z^w}$. The roots are computed using a modified version of fixed-point…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…
The fixed-point index of a homeomorphism of Jordan curves measures the number of fixed-points, with multiplicity, of the extension of the homeomorphism to the full Jordan domains in question. The now-classical Circle Index Lemma says that…
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrodinger's equation. Mathieu's equation can be easily solved…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
In this paper, we find the recursion formulas for generalized Lauricella matrix function. We also give the recursion formulas for the three variable Lauricella matrix functions.
It is known that difference equations generated as the Newton-Raphson iteration for quadratic equations are solvable in closed form, and the solution can be constructed from linear three-term recurrence relations with constant coefficients.…
A recurrence formula for absolute central moments of Poisson distribution is suggested.