On Fejér-type inequalities for generalized trigonometrically and hyperbolic k-convex functions

For , , and , where is an open interval of , we consider the set of functions satisfying the second-order differential inequality in . The considered set includes several classes of generalized convex functions from the literature. In particular, if and , , we obtain the class of trigonometrically -...

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Vydáno v:Demonstratio mathematica Ročník 57; číslo 1; s. 171 - 215
Hlavní autoři: Dragomir, Silvestru Sever, Jleli, Mohamed, Samet, Bessem
Médium: Journal Article
Jazyk:angličtina
Vydáno: De Gruyter 07.06.2024
Témata:
26A51
26D15
34B09
characterization
convex functions
differential inequalities
Fejér inequality
generalized convexity
hyperbolic
hyperbolic k-convex functions
trigonometrically
trigonometrically k-convex functions
ISSN:2391-4661, 2391-4661
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Popis
Shrnutí:For , , and , where is an open interval of , we consider the set of functions satisfying the second-order differential inequality in . The considered set includes several classes of generalized convex functions from the literature. In particular, if and , , we obtain the class of trigonometrically -convex functions, while if and , , we obtain the class of hyperbolic -convex functions. In this article, we establish a Fejér-type inequality for the introduced set of functions without any symmetry condition imposed on the weight function and discuss some special cases of weight functions. Moreover, we provide characterizations of the classes of trigonometrically and hyperbolic -convex functions.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2024-0001