Investigations into Hermite-Hadamard-Fejér Inequalities within the Realm of Trigonometric Convexity

This study is predicated on the exploration of lemmas pertaining to the Hermite-Hadamard-Fejér type integral inequality, focusing on both trapezoidal and midpoint inequalities. It delves into the realm of trigonometrically convex functions and is structured around the foundational lemmas that govern...

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Published in:Communications in advanced mathematical sciences (Online) Vol. 8; no. 1; pp. 36 - 48
Main Authors: Turhan, Sercan, Güngör, Ercihan, İşcan, İmdat
Format: Journal Article
Language:English
Published: Emrah Evren KARA 27.03.2025
Subjects:
h$-convex functions
hermite-hadamard-fejer type inequality
trigonometrically convex function
ISSN:2651-4001, 2651-4001
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Abstract This study is predicated on the exploration of lemmas pertaining to the Hermite-Hadamard-Fejér type integral inequality, focusing on both trapezoidal and midpoint inequalities. It delves into the realm of trigonometrically convex functions and is structured around the foundational lemmas that govern these inequalities. Through rigorous analysis, the research has successfully derived novel theorems and garnered insightful results that enhance the understanding of trigonometric convexity. Further, the study has undertaken the application of these theorems to exemplify trigonometrically convex functions, thereby providing practical instances that underline the theoretical developments. These applications not only serve to demonstrate the utility of the newly formulated results but also contribute to the broader field of convex analysis by introducing innovative perspectives on integral inequalities. The synthesis of theory and application encapsulated in this research marks a significant stride in the advancement of mathematical inequalities and their relevance to the study of convex functions.
AbstractList This study is predicated on the exploration of lemmas pertaining to the Hermite-Hadamard-Fejér type integral inequality, focusing on both trapezoidal and midpoint inequalities. It delves into the realm of trigonometrically convex functions and is structured around the foundational lemmas that govern these inequalities. Through rigorous analysis, the research has successfully derived novel theorems and garnered insightful results that enhance the understanding of trigonometric convexity. Further, the study has undertaken the application of these theorems to exemplify trigonometrically convex functions, thereby providing practical instances that underline the theoretical developments. These applications not only serve to demonstrate the utility of the newly formulated results but also contribute to the broader field of convex analysis by introducing innovative perspectives on integral inequalities. The synthesis of theory and application encapsulated in this research marks a significant stride in the advancement of mathematical inequalities and their relevance to the study of convex functions.
Author Turhan, Sercan
İşcan, İmdat
Güngör, Ercihan
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Cites_doi 10.14744/sigma.2021.00072
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10.1016/j.camwa.2009.07.073
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10.1186/s13660-023-02996-0
10.55730/1300-0098.3371
10.17776/csj.749571
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SubjectTerms h$-convex functions
hermite-hadamard-fejer type inequality
trigonometrically convex function
Title Investigations into Hermite-Hadamard-Fejér Inequalities within the Realm of Trigonometric Convexity
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