New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators
Abstract
1. Introduction
- 1.
- ;
- 2.
- ;
- 3.
- ;
- 4.
- ;
- 5.
- Γ is convex on
2. Preliminaries
3. Main Results
- 1.
- If we choose , and , then we have the inequality of Theorem 2 ( fractional integral type), and also, if we take , we obtain the classical inequality of Remark 1 in [55].
- 2.
- 3.
- If we take and , , then we obtain the well-known inequality for integral operators (Theorem 2.1) in [31].
- 4.
- If we choose and , and we have another important result obtained (namely Theorem 2.1) by Kian and Moslehian in [25].
- 5.
- If we choose and , and also, then we obtain the well-known inequality.
- 1.
- If we choose , and , then we have the inequality of Theorem 3 ( fractional integral type) in [55].
- 2.
- 3.
- If we take and , , then we obtain another form of inequality for integral operators (Teorem 2.3) in [31].
- 4.
- If we choose and , then we have another important result obtained by Kian and Moslehian in [25].
- 5.
- If we choose and , and also, then we obtain the well-known inequality.
4. Integral Identities Associated with the Main Results
5. Examples and Illustrations
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Yildiz, Ç.; İşleyen, T.; Cotîrlă, L.-I. New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators. Fractal Fract. 2025, 9, 343. https://doi.org/10.3390/fractalfract9060343
Yildiz Ç, İşleyen T, Cotîrlă L-I. New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators. Fractal and Fractional. 2025; 9(6):343. https://doi.org/10.3390/fractalfract9060343
Chicago/Turabian StyleYildiz, Çetin, Tevfik İşleyen, and Luminiţa-Ioana Cotîrlă. 2025. "New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators" Fractal and Fractional 9, no. 6: 343. https://doi.org/10.3390/fractalfract9060343
APA StyleYildiz, Ç., İşleyen, T., & Cotîrlă, L.-I. (2025). New Results on Majorized Discrete Jensen–Mercer Inequality for Raina Fractional Operators. Fractal and Fractional, 9(6), 343. https://doi.org/10.3390/fractalfract9060343