Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels
Abstract
:1. Introduction
2. Preliminaries
Fractional Integral Operators of Interval- and Fuzzy Number-Valued Mappings
3. Main Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Khan, M.B.; Macías-Díaz, J.E.; Althobaiti, A.; Althobaiti, S. Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels. Fractal Fract. 2023, 7, 567. https://doi.org/10.3390/fractalfract7070567
Khan MB, Macías-Díaz JE, Althobaiti A, Althobaiti S. Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels. Fractal and Fractional. 2023; 7(7):567. https://doi.org/10.3390/fractalfract7070567
Chicago/Turabian StyleKhan, Muhammad Bilal, Jorge E. Macías-Díaz, Ali Althobaiti, and Saad Althobaiti. 2023. "Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels" Fractal and Fractional 7, no. 7: 567. https://doi.org/10.3390/fractalfract7070567
APA StyleKhan, M. B., Macías-Díaz, J. E., Althobaiti, A., & Althobaiti, S. (2023). Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels. Fractal and Fractional, 7(7), 567. https://doi.org/10.3390/fractalfract7070567