Analysis of Maclaurin's inequality with applications in numerical analysis

Miguel Vivas-Cortez; Usama Asif; Muhammad Sakria Javed; Muhammad Uzair Awan; Badreddine  Meftah; Silvestru Sever Dragomir; Muhammad Aslam Noor

doi:10.7153/jmi-2025-19-86

Analysis of Maclaurin's inequality with applications in numerical analysis

Miguel Vivas-Cortez
, Usama Asif
, Muhammad Sakria Javed
, Muhammad Uzair Awan
, Badreddine Meftah
, Silvestru Sever Dragomir
, Muhammad Aslam Noor

Producción científica: Revista › Artículo › revisión exhaustiva

Resumen

Maclaurin’s inequality estimates the error bounds of a three-point open method named
as Maclaurin’s procedure. The current study aims to explore the error boundaries of Maclaurin’s
rule by utilizing the convexity of the mappings. We derive a new twice-differentiable Maclaurin’s
identity. Based on newly developed identity, the convexity of mappings, and the elementary
properties of inequalities, we derive some new Maclaurin’s type inequalities. Also, we apply the
obtained bounds to formulate the relation between means, composite quadrature bounds, and a
novel two-step iterative method with a cubic order of convergence. Lastly, we explore our major
findings and the iterative method through illustrative examples and visuals.

Idioma original	Inglés
Páginas (desde-hasta)	1349–1374
Número de páginas	26
Publicación	Journal of Mathematical Inequalities
Volumen	19
N.º	4
Fecha en línea anticipada	2025
DOI	https://doi.org/10.7153/jmi-2025-19-86 https://doi.org/10.7153/jmi-2025-19-86
Estado	Publicada - 24 dic. 2025

Nota bibliográfica

Publisher Copyright:
© 2025, Element D.O.O. All rights reserved.

Base de Datos Indexada

SCOPUS

Cuartil Publicación

NAQ2

Acceder al documento

10.7153/jmi-2025-19-86Licencia: CC BY-NC-ND
10.7153/jmi-2025-19-86

Otros archivos y enlaces

Enlace a la publicación en Scopus

Contemporary Theoretical Challenges and Practical Advances in Fractional and Generalized Calculus
Vivas Cortez, M. J. (Director), Guerrero, J. A. (Investigador Externo), Juan E., N. V. (Investigador Externo) & Velasco Velasco, J. (Investigador principal)
30/07/25 → 1/08/27
Proyecto: Investigación e Innovación

Citar esto

@article{1ff1a93dba4c4d42a3555a7e8bf48284,

title = "Analysis of Maclaurin's inequality with applications in numerical analysis",

abstract = "Maclaurin{\textquoteright}s inequality estimates the error bounds of a three-point open method named as Maclaurin{\textquoteright}s procedure. The current study aims to explore the error boundaries of Maclaurin{\textquoteright}s rule by utilizing the convexity of the mappings. We derive a new twice-differentiable Maclaurin{\textquoteright}s identity. Based on newly developed identity, the convexity of mappings, and the elementary properties of inequalities, we derive some new Maclaurin{\textquoteright}s type inequalities. Also, we apply the obtained bounds to formulate the relation between means, composite quadrature bounds, and a novel two-step iterative method with a cubic order of convergence. Lastly, we explore our major findings and the iterative method through illustrative examples and visuals.",

keywords = "26A51, 26D15, 32F99, 41A17, Convex functions, Euler-Maclaurin{\textquoteright}s inequality, H{\"o}lder{\textquoteright}s inequality, iterative scheme, Simspon{\textquoteright}s rule",

author = "Miguel Vivas-Cortez and Usama Asif and Javed, \{Muhammad Sakria\} and Awan, \{Muhammad Uzair\} and Badreddine Meftah and Dragomir, \{Silvestru Sever\} and Noor, \{Muhammad Aslam\}",

year = "2025",

month = dec,

day = "24",

doi = "10.7153/jmi-2025-19-86",

language = "English",

volume = "19",

pages = "1349–1374",

journal = "Journal of Mathematical Inequalities",

issn = "1846-579X",

publisher = "Element D.O.O.",

number = "4",

}

TY - JOUR

T1 - Analysis of Maclaurin's inequality with applications in numerical analysis

AU - Vivas-Cortez, Miguel

AU - Asif, Usama

AU - Javed, Muhammad Sakria

AU - Awan, Muhammad Uzair

AU - Meftah, Badreddine

AU - Dragomir, Silvestru Sever

AU - Noor, Muhammad Aslam

PY - 2025/12/24

Y1 - 2025/12/24

N2 - Maclaurin’s inequality estimates the error bounds of a three-point open method named as Maclaurin’s procedure. The current study aims to explore the error boundaries of Maclaurin’s rule by utilizing the convexity of the mappings. We derive a new twice-differentiable Maclaurin’s identity. Based on newly developed identity, the convexity of mappings, and the elementary properties of inequalities, we derive some new Maclaurin’s type inequalities. Also, we apply the obtained bounds to formulate the relation between means, composite quadrature bounds, and a novel two-step iterative method with a cubic order of convergence. Lastly, we explore our major findings and the iterative method through illustrative examples and visuals.

AB - Maclaurin’s inequality estimates the error bounds of a three-point open method named as Maclaurin’s procedure. The current study aims to explore the error boundaries of Maclaurin’s rule by utilizing the convexity of the mappings. We derive a new twice-differentiable Maclaurin’s identity. Based on newly developed identity, the convexity of mappings, and the elementary properties of inequalities, we derive some new Maclaurin’s type inequalities. Also, we apply the obtained bounds to formulate the relation between means, composite quadrature bounds, and a novel two-step iterative method with a cubic order of convergence. Lastly, we explore our major findings and the iterative method through illustrative examples and visuals.

KW - 26A51

KW - 26D15

KW - 32F99

KW - 41A17

KW - Convex functions

KW - Euler-Maclaurin’s inequality

KW - Hölder’s inequality

KW - iterative scheme

KW - Simspon’s rule

UR - https://www.scopus.com/pages/publications/105026984511

U2 - 10.7153/jmi-2025-19-86

DO - 10.7153/jmi-2025-19-86

M3 - Article

AN - SCOPUS:105026984511

SN - 1846-579X

VL - 19

SP - 1349

EP - 1374

JO - Journal of Mathematical Inequalities

JF - Journal of Mathematical Inequalities

IS - 4

ER -

Analysis of Maclaurin's inequality with applications in numerical analysis

Resumen

Nota bibliográfica

Base de Datos Indexada

Cuartil Publicación

Acceder al documento

Otros archivos y enlaces

Proyectos

Contemporary Theoretical Challenges and Practical Advances in Fractional and Generalized Calculus

Citar esto