Abstract
The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.
Highlights
The Hermite–Hadamard inequality is one of the most well-known inequalities in the theory of convex functions with geometrical meaning, and it has a wide range of applications
The Hermite–Hadamard inequality (H.H inequality) for convex functions has gotten a lot of attention, and there have been some impressive improvements and generalizations, see [1,2]
Interval analysis is a special instance that was developed to deal with interval uncertainty that may be found in many mathematical or computer models of deterministic real-world processes
Summary
The Hermite–Hadamard inequality is one of the most well-known inequalities in the theory of convex functions with geometrical meaning, and it has a wide range of applications. This disparity might be seen as a refinement of the idea of convexity. The relevance of set-valued analysis research from both a theoretical and practical standpoint is well understood. Control theory and dynamical games have fueled several developments in set-valued analysis. A few major inequalities for interval-valued functions, such as H.H and Ostrowski type inequalities have been developed. Chalco-Cano et al used Hukuhara derivatives for interval-valued functions to develop Ostrowski type inequalities for intervalvalued functions in [3,4]. Readers [6–13] are referred to for further relevant findings
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
