(q<sub>1</sub>,q<sub>2</sub>)-Trapezium-Like Inequalities Involving Twice Differentiable Generalized m-Convex Functions and Applications
oleh: Muhammad Uzair Awan, Muhammad Zakria Javed, Ibrahim Slimane, Artion Kashuri, Clemente Cesarano, Kamsing Nonlaopon
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2022-08-01 |
Deskripsi
A new auxiliary result pertaining to twice (<inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">q</mi><mn>1</mn></msub><mo>,</mo><msub><mi mathvariant="normal">q</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>)-differentiable functions is derived. Using this new auxiliary result, some new versions of Hermite–Hadamard’s inequality involving the class of generalized <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi mathvariant="fraktur">m</mi></semantics></math></inline-formula>-convex functions are obtained. Finally, to demonstrate the significance of the main outcomes, some applications are discussed for hypergeometric functions, Mittag–Leffler functions, and bounded functions.