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

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

M. Soni, R. K. Sharma, S. Sharma — Sun, 29 Dec 2024 00:00:00 +0700

This study investigates the impact of both detected and undetected viral cases, alongside environmental pathogens, on infection transmission dynamics. A VSEIQCR model is formulated and refined to analyze the study and to assess the basic reproduction number using the next-generation matrix method. The findings reveal a rapid escalation in viral cases, correlating with the rise in undetected cases. The study suggests that identifying and isolating individuals exposed to or infected by the virus, whether detected or undetected, is deemed imperative for curtailing disease transmission. Additionally, The study emphasizes the role of fomites in infection spread. It stands out for its innovative approach, examining the interconnections among vaccination, quarantine, and contamination strategies within a cohesive research framework, thereby setting a precedent in the field.

CONVERGENCE BEHAVIOR OF MODIFIED-BERNSTEIN-KANTROVINCH-STANCU OPERATORS

S. Sonker, P. Moond, B. B. Jena, S. K. Paikray — Sun, 29 Dec 2024 00:00:00 +0700

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

S. S. Handibag , J.H. Bhosale — Sun, 29 Dec 2024 00:00:00 +0700

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 α-ψ-φ-F-CONTRACTIVE MAPPINGS IN QUASI-b-METRIC-LIKE SPACES

J. G. Kadwin, S. I. Raj, D.M. Jiny — Sun, 29 Dec 2024 00:00:00 +0700

In this paper, we introduce some new generalized mappings in quasi-b-metric-like spaces and establish some fixed point theorems with concrete examples. Our results generalize fixed point results in the literature.

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

S. Temir — Sun, 29 Dec 2024 00:00:00 +0700

In this paper, we study the convergence of the SP*-iteration process to fixed point for operators with property (E) in CAT(0) spaces. We also prove the stability of the SP*-iteration process 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

S. Park — Sun, 29 Dec 2024 00:00:00 +0700

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.