arXiv subjects

Ivan Hadinata

Publications and source records attributed to Ivan Hadinata.

3 recordsLinked to original sources

arXiv2026

Partial extended b-metric and some fixed point theorem

In this paper, we introduce the concept of partial extended b-metric spaces (PEBMS) as a unification and generalization of extended b-metric spaces and partial b-metric spaces. This new structure incorporates a point-dependent control function together with the possibility of non-zero self-distance, providing a more flexible framework for the study of generalized metric spaces. We establish several fundamental properties of PEBMS, including convergence, Cauchy sequences, and 0-completeness. By introducing the notion of 0-Cauchy sequences, we extend various results from extended b-metric spaces to the PEBMS setting. In particular, we prove fixed point theorems for contractive mappings and show the existence and uniqueness of fixed points under suitable conditions. Furthermore, we demonstrate that every extended b-metric space can be viewed as a special case of a PEBMS. As an application, we study the stability of discrete dynamical systems within this framework. The results presented here generalize and enrich existing theories in metric-type spaces and open new directions for further research.

math.FA↗

arXiv2025

Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum

In this paper, we present the existence and uniqueness property on a finite sum involving a polynomial and a homogeneous linear recurrence sequence. This finite sum is of the form $\sum_{k=1}^n P(k)s_{hk+r}$ where $n$ is a positive integer, $P(x)$ is a polynomial in $\mathbb C[x]$, $h$ and $r$ are some integers, and $(s_k)_{k\in\mathbb Z}$ is a homogeneous linear recurrence sequence of degree $m\geq 2$ with some constraints.

math.NT↗

arXiv2025

On Sum of a Polynomial Multiplied by Generalized Fibonacci Numbers

Given that $a,b\in\mathbb N$, $c_0,c_1\in\mathbb Z$, $(c_0,c_1)\neq (0,0)$, and a generalized Fibonacci sequence $(s_n)_{n\geq 0}$ where $s_0 = c_0$, $s_1 = c_1$, and $s_{n+1}=as_{n}+bs_{n-1}$ for all positive integers $n$. In this paper, we get the result that for every polynomials $P(x)$ with real coefficients, we can always find three polynomials $F_1(x), G_1(x), H_1(x)$ (not necessarily distinct) with real coefficients satisfying the identity: $\;2\sum_{k=1}^{n}P(k)s_{k-1} = F_1(n)s_{n+1} + G_1(n)s_n + H_1(n), \;\forall n\in\mathbb N$. Furthermore, we serve two constraints for $(s_n)_{n\geq 0}$: one constraint implies that there are infinitely many triples $(F_1(x), G_1(x), H_1(x))$ satisfying the identity $\;2\sum_{k=1}^{n}P(k)s_{k-1} = F_1(n)s_{n+1} + G_1(n)s_n + H_1(n), \;\forall n\in\mathbb N$, while another constraint implies that there is only one triple $(F_1(x), G_1(x), H_1(x))$ satisfying the identity $\;2\sum_{k=1}^{n}P(k)s_{k-1} = F_1(n)s_{n+1} + G_1(n)s_n + H_1(n), \;\forall n\in\mathbb N$.

math.NT↗