Related papers: Fibonacci Numbers, Statistical Convergence and App…
The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on…
We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
The research aims to construct a new type of matrix called the Fibonacci-Hessenberg-Lorentz matrix by multiplying Fibonacci-Hessenberg matrices with Lorentz matrix multiplication. The study will start by examining the properties of…
Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subsequent terms are determined by the sum of the preceding k terms.…
The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the…
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
A Redheffer--type matrix with Fibonacci entries is defined, and the determinant and spectral properties of this matrix are studied. Also, more general Redheffer--type matrices are considered and intriguing number-theoretic examples are…
In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function $f$ is Abel statistically continuous on a subset $E$ of $\R$, the set of real numbers, if it preserves Abel statistical convergent…
We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze…
In this research article, we have primarily focused on the circumstantial investigation of deferred statistical convergence of sequences and investigated some fundamental results compatible with the structure of a probabilistic normed…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation…
In this note we introduce and define half Cauchy sequences. We prove that a sequence of real numbers is convergent if and only if it is bounded and half Cauchy. We also provide an example of how the concept may be used.
The paper investigates relationship between algebraic expressions and graphs. We consider a digraph called a Fibonacci graph which gives a generic example of non-series-parallel graphs. Our intention in this paper is to simplify the…
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally,…
The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…