New Class Up and Down <inline-formula><math display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-Convex Fuzzy-Number Valued Mappings and Related Fuzzy Fractional Inequalities

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.

Keywords

• fuzzy-number valued mappings
• fuzzy integrals
• up and down <i>λ</i>-convex fuzzy-number valued mappings
• fuzzy Hermite–Hadamard type inequalities