Related papers: Fibonacci Numbers, Statistical Convergence and App…
Statistical convergence was introduced in connection with problems of series summation. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with…
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.
In this paper, we study the concept of Fibonacci statistical convergence on intuitionisitic fuzzy normed space. We define the Fibonacci statistically Cauchy sequences with respect to an intuitionisitic fuzzy normed space and introduce the…
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…
Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of…
Here we have discussed on Fermi-Dirac statistics, in particular, on its brief historical progress, derivation, consequences, applications, etc. Importance of Fermi-Dirac statistics has been discussed even in connection with the current…
We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of…
In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
The following article summarizes research where theorems and their respective demonstrations are postulated based on quadratic equations with special properties given by the Pythagorean triplets and the Fibonacci sequence given the second…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…