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 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.