Abstract
The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. The newly suggested mappings are then used to create certain Hermite–Hadamard- and Pachpatte-type integral fuzzy inclusion relations in fuzzy fractional calculus. It is also suggested to revise the Hermite–Hadamard integral fuzzy inclusions with regard to the up and down λ-convex fuzzy-number valued mappings (U∙D λ-convex F-N∙V∙Ms). Moreover, Hermite–Hadamard–Fejér has been proven, and some examples are given to demonstrate the validation of our main results. The new and exceptional cases are presented in terms of the change of the parameters “i” and “α” in order to assess the accuracy of the obtained fuzzy inclusion relations in this study.
Funder
Spanish Ministerio de Ciencia e Innovación
Taif University Researchers Supporting Project
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Reference95 articles.
1. On q-Hermite-Hadamard inequalities for general convex mappings;Acta Math. Hungar.,2020
2. On Fejer type inequalities for convex mappings utilizing fractional integrals mapping with respect to another mapping;Results Math.,2019
3. Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals;J. Math. Anal. Appl.,2017
4. On the Bullen-type inequalities via generalized fractional integrals and their applications;Fractals,2021
5. Weighted Hermite-Hadamard-Mercer type inequalities for convex mappings;Numer. Methods Partial Differential Eq.,2021