Research Article

Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications

Volume: 9 Number: 2 June 30, 2026
Fundamental Journal of Mathematics and Applications Cover
Fundamental Journal of Mathematics and Applications
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Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications

Abstract

In mathematical analysis, the theory of inequalities plays a crucial roledue to its wide applications across various fields of physical sciences. Inthis article, we develop a new class of fractional Bullen-type inequalitiesrelated to the Jensen-Mercer inequality. To achieve this, first, we obtain ageneral fractional Bullen-Mercer identity that plays the foundation for ourmain results. Additionally, using the fractional Bullen-Mercer equality andapplying properties of $s$-convex functions, we give several newinequalities using H\"{o}lder's, power-mean and Young's inequalities. Someknown results are recaptured and several special cases are discussed indetail. Furthermore, applying Lipschitzian and bounded functions in ourgeneral fractional Bullen-Mercer identity, we present some new inequalities.Moreover, we offer some applications of our results, including their use inspecial means, error bounds, matrix inequality and the $q$-digamma function.To validate our findings, we perform various simulations.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Publication Date

June 30, 2026

Submission Date

January 8, 2026

Acceptance Date

May 5, 2026

Published in Issue

Year 2026 Volume: 9 Number: 2

DOI

https://doi.org/10.33401/fujma.1859149

IZ

https://izlik.org/JA92RP94LA

Cite

RIS / Bibtex
APA
Munir, A., Kashuri, A., & Hezenci, F. (2026). Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications. Fundamental Journal of Mathematics and Applications, 9(2), 63-78. https://doi.org/10.33401/fujma.1859149
AMA
1.Munir A, Kashuri A, Hezenci F. Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications. Fundam. J. Math. Appl. 2026;9(2):63-78. doi:10.33401/fujma.1859149
Chicago
Munir, Arslan, Artion Kashuri, and Fatih Hezenci. 2026. “Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ S $-Convex Functions and Numerical Applications”. Fundamental Journal of Mathematics and Applications 9 (2): 63-78. https://doi.org/10.33401/fujma.1859149.
EndNote
Munir A, Kashuri A, Hezenci F (June 1, 2026) Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications. Fundamental Journal of Mathematics and Applications 9 2 63–78.
IEEE
[1]A. Munir, A. Kashuri, and F. Hezenci, “Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications”, Fundam. J. Math. Appl., vol. 9, no. 2, pp. 63–78, June 2026, doi: 10.33401/fujma.1859149.
ISNAD
Munir, Arslan - Kashuri, Artion - Hezenci, Fatih. “Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ S $-Convex Functions and Numerical Applications”. Fundamental Journal of Mathematics and Applications 9/2 (June 1, 2026): 63-78. https://doi.org/10.33401/fujma.1859149.
JAMA
1.Munir A, Kashuri A, Hezenci F. Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications. Fundam. J. Math. Appl. 2026;9:63–78.
MLA
Munir, Arslan, et al. “Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ S $-Convex Functions and Numerical Applications”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 2, June 2026, pp. 63-78, doi:10.33401/fujma.1859149.
Vancouver
1.Arslan Munir, Artion Kashuri, Fatih Hezenci. Advances in Fractional Bullen-Mercer Type Inequalities: Analysis via Differentiable $ s $-Convex Functions and Numerical Applications. Fundam. J. Math. Appl. 2026 Jun. 1;9(2):63-78. doi:10.33401/fujma.1859149

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