Some new versions of Jensen, Schur and Hermite-Hadamard type inequalities for ( p , J ) " role="presentation"> ( p , J ) ( p , J ) \left({p}, \mathfrak{J}\right) -convex fuzzy-interval-valued functions

AIMS Mathematics

article

Muhammad Bilal Khan¹  Gustavo Santos-García²  Hüseyin Budak³  Savin Treanțǎ⁴  Mohamed S. Soliman⁵ 

[1] Department of Mathematics, COMSATS University Islamabad;Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise ,(IME), University of Salamanca;Department of Mathematics, Faculty of Science and Arts, Düzce University;Department of Applied Mathematics, University Politehnica of Bucharest;Department of Electrical Engineering, College of Engineering, Taif University

关键词: $ \left(\mathfrak{p};    \mathfrak{J}\right) $-convex fuzzy-interval-valued function;    fuzzy Riemann integral;    Jensen type inequality;    Schur type inequality;    Hermite-Hadamard type inequality;    Hermite-Hadamard-Fejér type inequality;   

DOI  :  10.3934/math.2023374

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

To create various kinds of inequalities, the idea of convexity is essential. Convexity and integral inequality hence have a significant link. This study's goals are to introduce a new class of generalized convex fuzzy-interval-valued functions (convex ????s) which are known as $ \left(\mathfrak{p}, \mathfrak{J}\right) $-convex ????s and to establish Jensen, Schur and Hermite-Hadamard type inequalities for $ \left(\mathfrak{p}, \mathfrak{J}\right) $-convex ????s using fuzzy order relation. The Kulisch-Miranker order relation, which is based on interval space, is used to define this fuzzy order relation level-wise. Additionally, we have demonstrated that, as special examples, our conclusions encompass a sizable class of both new and well-known inequalities for $ \left(\mathfrak{p}, \mathfrak{J}\right) $-convex ????s. We offer helpful examples that demonstrate the theory created in this study's application. These findings and various methods might point the way in new directions for modeling, interval-valued functions and fuzzy optimization issues.

【 授权许可】

CC BY