Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

FOMITE FACTORS AND SILENT SPREAD: A VSEIQCR STUDY OF VIRAL DISEASES

MOHIT SONI — 2024-12-29

This study investigated the impact of both detected and undetected viral
cases, along with environmental pathogens, on infection transmission dynamics. A
VSEIQCR model was formulated and refined to assess the basic reproduction number
through the next-generation matrix method. Findings reveal a rapid escalation in viral
cases correlating with the rise in undetected cases. The identification and isolation of
individuals exposed to and infected by the virus, whether detected or undetected, are
deemed imperative for curtailing disease transmission. Additionally, understanding the
role of fomites in infection spread is emphasized.This study stands out for its innovative
approach, examining the interconnections among vaccination, quarantine, and contaminated
strategies within a cohesive research framework, setting a precedent in the field.

Convergence Behavior of Modified-Bernstein-Kantrovinch-Stancu Operators

Susanta Kumar Paikray — 2024-12-29

The study introduces a Kantrovinch-Stancu type modification of the modified-Bernstein operator, examining its convergence properties for H\"{o}lder's class of functions. It evaluates the rate of convergence through the modulus of continuity and Peetre's K-functional, providing insights into the efficiency of the proposed operators. Additionally, the research establishes a Vornovskaya type asymptotic result and investigates weighted approximation with polynomial growth, shedding light on the behavior of approximations under varying conditions. To illustrate the convergence behavior empirically, the study employs MATLAB software to present numerical examples, offering tangible evidence of the theoretical findings. Through this comprehensive analysis, the study contributes to understanding the performance and applicability of the Kantrovinch-Stancu modification in approximation theory, with implications for various fields relying on function approximation techniques.

A comparative study of Laplace decomposition method and Variational iteration method for solving nonlinear integro -differential equations

jyoti bhosale — 2024-12-29

In this study, we compare the Laplace decomposition approach to the variational iteration method.

This research focuses on comparing methodologies to resolve integro-differential equations that are nonlinear.The result show how practical and successful these methods are. We compare the results to four cases to assess the solution's correctness.

Generalized $\alpha$-$\psi$-$\varphi$-$F$-contractive mappings in quasi-$b$-metric like spaces

Iruthaya Raj Saminathan — 2024-12-29

Respected editor,

I have submitted a research paper entiled, "Generalized $\alpha$-$\psi$-$\varphi$-$F$-contractive mappings in quasi-$b$-metric like spaces" to your journal. Kindly consider the paper to publish in your journal.

CONVERGENCE THEOREMS FOR OPERATORS WITH PROPERTY (E) IN CAT(0) SPACES

Seyit Temir — 2024-12-29

In this paper, we study the convergence of the SP*-iteration
to fixed point for operators with property $(E)$ in $CAT(0)$ spaces. Our results improve and extend some recently results in the literature of fixed point theory in $CAT(0)$ spaces.

New applications of the metatheorem in ordered fixed point theory

Sehie Park — 2024-12-29

Our aim in this paper is to and new applications of our long- standing 2023 Metatheorem. In fact, a certain particular form of Metatheorem on fixed point theorems characterizes metric completeness. Moreover, classical theorems due to Banach, Rus-Hicks-Rhoades, Nadler, Covitz-Nadler, Oettli- Thera, Edelstein, Turinici, Taskovic, Khamsi and ourselves are equivalently formulated or improved by applying Metatheorem.