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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Bibliographic Details
Published in:Demonstratio mathematica Vol. 57; no. 1; pp. 171 - 215
Main Authors: Dragomir, Silvestru Sever, Jleli, Mohamed, Samet, Bessem
Format: Journal Article
Language:English
Published: De Gruyter 07.06.2024
Subjects:
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
Online Access:Get full text
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Summary: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