New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

Author:

Alreshidi Nasser Aedh1ORCID,Khan Muhammad Bilal2,Breaz Daniel3,Cotirla Luminita-Ioana4ORCID

Affiliation:

1. Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia

2. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania

3. Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania

4. Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Abstract

It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

Funder

Deanship of Scientific Research at Northern Border University, Arar, Saudi Arabia

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference90 articles.

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2. Mitrinovíc, D.S. (1970). Analytic Inequalities, Springer.

3. The Minkowski’s inequalities via Riemann-Liouville fractional integral operators;Aljaaidi;Rend. Circ. Mat. Palermo Ser. B,2021

4. Some new refinements of Hermite-Hadamard-type inequalities Involving-Riemann-Liouville fractional integrals and applications;Awan;Math. Probl. Eng.,2020

5. Hermite-Hadamard and Hermite-Hadamard-Fejr type inequalities for generalized fractional integrals;Chen;J. Math. Anal. Appl.,2017

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