On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings

Sinan Aslan; Abdelghani Lakhdari

On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings

Abstract

In this paper, we employ a particular identity for twice differentiable functions that has been established in the literature to derive several new fractional Milne-type inequalities for functions whose second-order derivatives in absolute value exhibit strong $m-$convexity and strong $(\alpha,m)$-convexity. Moreover, by applying Hölder’s and Young’s inequalities to these classes of functions, we derive additional significant results that contribute to the existing theory.

Keywords

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Sinan Aslan
0000-0001-5970-1926
Türkiye

Abdelghani Lakhdari ^*
0000-0003-2943-2678
Türkiye

Publication Date

June 5, 2026

Submission Date

January 27, 2026

Acceptance Date

May 16, 2026

Published in Issue

Year 2026 Volume: 2 Number: 1

IZ

https://izlik.org/JA59HG98EW

Cite

RIS / Bibtex

APA

Aslan, S., & Lakhdari, A. (2026). On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings. Düzce Mathematical Research, 2(1), 1-19. https://izlik.org/JA59HG98EW

AMA

1.Aslan S, Lakhdari A. On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings. Düzce Mathematical Research. 2026;2(1):1-19. https://izlik.org/JA59HG98EW

Chicago

Aslan, Sinan, and Abdelghani Lakhdari. 2026. “On Fractional Milne-Type Inequalities for Strongly $m$-Convex and Strongly $(\alpha,m)$- Convex Mappings”. Düzce Mathematical Research 2 (1): 1-19. https://izlik.org/JA59HG98EW.

EndNote

Aslan S, Lakhdari A (June 1, 2026) On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings. Düzce Mathematical Research 2 1 1–19.

IEEE

[1]S. Aslan and A. Lakhdari, “On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings”, Düzce Mathematical Research, vol. 2, no. 1, pp. 1–19, June 2026, [Online]. Available: https://izlik.org/JA59HG98EW

ISNAD

Aslan, Sinan - Lakhdari, Abdelghani. “On Fractional Milne-Type Inequalities for Strongly $m$-Convex and Strongly $(\alpha,m)$- Convex Mappings”. Düzce Mathematical Research 2/1 (June 1, 2026): 1-19. https://izlik.org/JA59HG98EW.

JAMA

1.Aslan S, Lakhdari A. On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings. Düzce Mathematical Research. 2026;2:1–19.

MLA

Aslan, Sinan, and Abdelghani Lakhdari. “On Fractional Milne-Type Inequalities for Strongly $m$-Convex and Strongly $(\alpha,m)$- Convex Mappings”. Düzce Mathematical Research, vol. 2, no. 1, June 2026, pp. 1-19, https://izlik.org/JA59HG98EW.

Vancouver

1.Sinan Aslan, Abdelghani Lakhdari. On fractional Milne-type inequalities for strongly $m$-convex and strongly $(\alpha,m)$- convex mappings. Düzce Mathematical Research [Internet]. 2026 Jun. 1;2(1):1-19. Available from: https://izlik.org/JA59HG98EW