Name
Title | ||
|---|---|---|
Integral Inequalities for Generalized Harmonically Convex Functions in Fuzzy-Interval-Valued Settings |
Abstract | ||
|---|---|---|
It is a well-known fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity also plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from both the concepts, owing to the significant correlation that has developed between both in recent years. In this paper, we introduce a new class of harmonically convex fuzzy-interval-valued functions which is known as harmonically h-convex fuzzy-interval-valued functions (abbreviated as harmonically h-convex F-I-V-Fs) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch-Miranker order relation defined on interval space. Some properties of this class are investigated. BY using fuzzy order relation and h-convex F-I-V-Fs, Hermite-Hadamard type inequalities for harmonically are developed via fuzzy Riemann integral. We have also obtained some new inequalities for the product of harmonically h-convex F-I-V-Fs. Moreover, we establish Hermite-Hadamard-Fej'er inequality for harmonically h-convex F-I-V-Fs via fuzzy Riemann integral. These outcomes are a generalization of a number of previously known results, as well as many new outcomes can be deduced as a result of appropriate parameter "theta " and real valued function " backward difference " selections. For the validation of the main results, we have added some nontrivial examples. We hope that the concepts and techniques of this study may open new directions for research. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.3390/sym13122352 | SYMMETRY-BASEL |
Keywords | DocType | Volume |
harmonically h-convex fuzzy interval-valued function, fuzzy Riemannian integral, Hermite-Hadamard inequality, Hermite-Hadamard Fejer inequality | Journal | 13 |
Issue | Citations | PageRank |
12 | 1 | 0.36 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Muhammad Bilal Khan | 1 | 7 | 3.26 |
| Pshtiwan Othman Mohammed | 2 | 1 | 1.38 |
| José António Tenreiro Machado | 3 | 1 | 0.36 |
| Juan Luis García Guirao | 4 | 1 | 0.36 |