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Volume 14
Issue 12
10.3390/axioms14120897
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means

by
Muhammad Muddassar
1,
Maria Bibi
1,
Kashif Nazar
2 and
Adil Jhangeer
3,4,5,*
1
Department of Mathematical Sciences, University of Engineering and Technology, Taxila 47050, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
3
IT4-Innovations, VSB-Technical University of Ostrava, 708 00 Ostrava-Poruba, Czech Republic
4
Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku AZ 1096, Azerbaijan
5
Department of Computer Engineering, Biruni University, Istanbul 34015, Turkey
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(12), 897; https://doi.org/10.3390/axioms14120897 (registering DOI)
Submission received: 22 October 2025 / Revised: 24 November 2025 / Accepted: 26 November 2025 / Published: 2 December 2025
(This article belongs to the Special Issue Generalized Fractional Operators and Special Functions: Theory, Methods, and Applications)
Versions Notes

Abstract

This article introduces certain algebraic properties of generalized (h˜1,h˜2)-pre-invex functions on Rℵ(0<ℵ≤1). A new fractal weighted integral identity is established and further employed to obtain several Ostrowski-type results in the fractal setting for functions whose first derivatives in the modulus belong to the generalized (h˜1,h˜2)-pre-invex functions’s class. An illustrative example is presented to validate the theoretical findings. Moreover, applications of the main results are derived in connection with generalized random variables and various special means, highlighting the effectiveness and potential scope of the proposed approach.
Keywords: local fractional integrals; generalized (h˜1,h˜2)-pre-invex functions; fractal sets; Ostrowski-type inequality local fractional integrals; generalized (h˜1,h˜2)-pre-invex functions; fractal sets; Ostrowski-type inequality

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MDPI and ACS Style

Muddassar, M.; Bibi, M.; Nazar, K.; Jhangeer, A. Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means. Axioms 2025, 14, 897. https://doi.org/10.3390/axioms14120897

AMA Style

Muddassar M, Bibi M, Nazar K, Jhangeer A. Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means. Axioms. 2025; 14(12):897. https://doi.org/10.3390/axioms14120897

Chicago/Turabian Style

Muddassar, Muhammad, Maria Bibi, Kashif Nazar, and Adil Jhangeer. 2025. "Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means" Axioms 14, no. 12: 897. https://doi.org/10.3390/axioms14120897

APA Style

Muddassar, M., Bibi, M., Nazar, K., & Jhangeer, A. (2025). Fractal Modeling of Generalized Weighted Pre-Invex Functions with Applications to Random Variables and Special Means. Axioms, 14(12), 897. https://doi.org/10.3390/axioms14120897

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