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Axioms
Volume 15
Issue 6
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Axioms, Volume 15, Issue 6 (June 2026) – 2 articles

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39 pages, 1158 KB  
Article
Minification Integer-Valued Split-BREAK Process with Power Series Innovations and Application in Fire Safety Dynamics
by Vladica S. Stojanović, Nikola Mitrović, Kristina Tomović, Hassan S. Bakouch and Shuhrah Alghamdi
Axioms 2026, 15(6), 388; https://doi.org/10.3390/axioms15060388 (registering DOI) - 22 May 2026
Abstract
This manuscript introduces a new class of count time series models, referred to as the minification integer-valued Split-BREAK (MIN–SB) process. The proposed framework extends the Split-BREAK modeling philosophy to the integer-valued setting and provides a flexible mechanism for capturing rare events, zero inflation, [...] Read more.
This manuscript introduces a new class of count time series models, referred to as the minification integer-valued Split-BREAK (MIN–SB) process. The proposed framework extends the Split-BREAK modeling philosophy to the integer-valued setting and provides a flexible mechanism for capturing rare events, zero inflation, and structural regime changes frequently observed in safety-related data. The main stochastic properties of the MIN–SB process are derived, including stationarity conditions, explicit moment structure, and correlation dynamics. A key theoretical result reveals an implicit hidden Markov structure underlying the observable process, providing a structural explanation for zero clustering observed in rare-event count processes. Parameter estimation is developed using a simulated method of moments (SMM) approach based on zero-related statistics, and the asymptotic properties of the resulting estimators are established. A Monte Carlo simulation study demonstrates favorable finite-sample performance of the proposed estimation procedure. The practical usefulness of the model is illustrated through an empirical application to time series of injuries and fatalities caused by fire accidents in Serbia. The results show that the MIN–SB specification provides a flexible and accurate framework for modeling zero-inflated count processes arising in fire safety dynamics. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods and Their Applications, 3rd Edition)
11 pages, 257 KB  
Article
New Results on Fixed Points and Coupled Fixed Points for α-Admissible Condensing Operators
by Taoufik Moulahi and Najmeddine Attia
Axioms 2026, 15(6), 387; https://doi.org/10.3390/axioms15060387 - 22 May 2026
Abstract
This paper introduces a novel class of condensing mappings through the concept of α-admissibility. We prove several extensions of Darbo’s fixed point theorem within this framework, including a generalized contractive condition and a coupled fixed point result. Our main results extend the [...] Read more.
This paper introduces a novel class of condensing mappings through the concept of α-admissibility. We prove several extensions of Darbo’s fixed point theorem within this framework, including a generalized contractive condition and a coupled fixed point result. Our main results extend the classical condensing condition to a flexible inequality involving α-admissibility and an auxiliary function. An example is given to demonstrate the applicability of our theorems where traditional approaches fail. Also, by leveraging the properties of α-admissible condensing operators, we proceed to establish a coupled fixed point theorem that relaxes traditional compactness conditions. At the end of the article, we apply our main theorem to prove the existence of solutions for a nonlinear integral equation. Full article
(This article belongs to the Section Mathematical Analysis)
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