Generalized Fractional Integral Inequalities for p-Convex Fuzzy Interval-Valued Mappings
Abstract
:1. Introduction
2. Preliminaries
- (1)
- should be normal ifand
- (2)
- should be upper-semicontinuous onif for givenandsuch thatfor allwith
- (3)
- should be fuzzy-convex, that isfor alland
- (4)
- should be compactly supported, that isis compact.
2.1. Fractional Integral Operators of Interval- and Fuzzy-Interval-Valued Mappings
2.2. Fuzzy-Interval-Valued Convexities
- p-convex onif
- p-concave onif inequality (23) is reversed.
3. Fuzzy Fractional-Interval-Valued Hermite–Hadamard Inequalities
4. Conclusions and Future Plans
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
fuzzy-interval-valued functions | f-i-v-ms |
interval-valued functions | i-v-ms |
Hermite–Hadamard inequality | – inequality |
Hermite–Hadamard–Fejér inequality | ––Fejér inequality |
Aumann integrable | IA-integrable |
interval | |
set of intervals | |
order relation defined on | |
set of fuzzy sets | |
set of fuzzy numbers or intervals | |
order relation defined on |
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Khan, M.B.; Cătaș, A.; Saeed, T. Generalized Fractional Integral Inequalities for p-Convex Fuzzy Interval-Valued Mappings. Fractal Fract. 2022, 6, 324. https://doi.org/10.3390/fractalfract6060324
Khan MB, Cătaș A, Saeed T. Generalized Fractional Integral Inequalities for p-Convex Fuzzy Interval-Valued Mappings. Fractal and Fractional. 2022; 6(6):324. https://doi.org/10.3390/fractalfract6060324
Chicago/Turabian StyleKhan, Muhammad Bilal, Adriana Cătaș, and Tareq Saeed. 2022. "Generalized Fractional Integral Inequalities for p-Convex Fuzzy Interval-Valued Mappings" Fractal and Fractional 6, no. 6: 324. https://doi.org/10.3390/fractalfract6060324