fixed point

Abstract. M.Akram et al. ([1],[2]) have introduced a larger class of mappings called A-contraction, which is a proper superclass of Kannan’s [7], Bianchini’s [3] and Reich’s [8] type contractions. In the present paper, we have proved some fixed point theorems for A-contraction mappings in a 2-metric space.

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

In this paper the problem of the number of fixed points for an RSA algorithm is considered. This is an important question from the point of view of any cryptosystem. We have estimated the expected value of this number for randomly chosen RSA parameters. It turned out that it is O(ln2n), and the probability of finding such a point is O(ln2n/n). Thus, these values are really negligible, which had been intuitively expected.

It has been recently investigated that the jerk dynamical systems are the simplest ever systems, which possess variety of dynamical behaviors including chaotic motion. Interestingly, the jerk dynamical systems also describe various phenomena in physics and engineering such as electrical circuits, mechanical oscillators, laser physics, solar wind driven magnetosphere ionosphere (WINDMI) model, damped harmonic oscillator driven by nonlinear memory term,

Abstract:-This work is based on a previous FFHSS (Fast Frequency Hopping Spread Spectrum) transceiver designed for wireless optical communications. The core of the transmitter is a discrete DDS (Direct Digital Synthesizer). In the first prototype the DDS control and the digital synchronization signal were generated using a PLD (Programmable Logic Device), besides a discrete external filter was necessary to eliminate high frequency components of digital synchronization signal and generated analog synchronization ...

In this paper we prove common fixed point theorems in fuzzy metric spaces employing the notion of reciprocal continuity. Moreover we have to show that in the context of reciprocal continuity the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.

In this paper we study the ergodic theory of a class of symbolic dynamical systems $(\O, T, \mu)$ where $T:{\O}\to \O$ the left shift transformation on $\O=\prod_0^\infty\{0,1\}$ and $\mu$ is a $\s$-finite $T$-invariant measure having the property that one can find a real number $d$ so that $\mu(\tau^d)=\infty$ but $\mu(\tau^{d-\epsilon}) 0$, where $\tau$ is the first passage time function in the reference state 1. In particular we shall consider invariant measures $\mu$ arising from a potential $V$ which is uniformly continuous but not of summable variation. If $d>0$ then $\mu$ can be normalized to give the unique non-atomic equilibrium probability measure of $V$ for which we compute the (asymptotically) exact mixing rate, of order $n^{-d}$. We also establish the weak-Bernoulli property and a polynomial cluster property (decay of correlations) for observables of polynomial variation. If instead $d\leq 0$ then $\mu$ is an infinite measure with scaling rate of order $n^d$. Moreove...

A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the dynamic system with the set of the local minima of the energy functional, have been determined. The influence of the connection matrix diagonal elements on the structure of the fixed points set has been investigated.

In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous maps. A counter-example is given to justify our requirement. As an application, we establish an existence result for a Hammerstein integral equation in a Banach space.