Abstract
In this manuscript, we utilize s-and Green convex functions to obtain a bound for the Jensen gap in discrete form and a bound for the Jensen gap in integral form. As an application of the discrete result, we derive a converse of the Holder inequality. Based on the integral result, we obtain a bound for the Hermite Hadamard gap and present a converse of the Holder inequality in its integral version. Also, we present bounds for Csiszar and Renyi divergences as applications of the discrete result. Finally, we utilize the bound obtained for Csiszar divergence, and deduce new estimates for other divergences in information theory.
Highlights
Convex functions and their generalizations play a significant role in scientific observation and calculation of various parameters in modern analysis, especially in the theory of optimization
We provide a converse of the Hölder inequality in integral form as an application of Theorem 2.3
The Jensen inequality has numerous applications in engineering, economics, computer science, information theory, and coding; it has been derived for convex and generalized convex functions
Summary
Convex functions and their generalizations play a significant role in scientific observation and calculation of various parameters in modern analysis, especially in the theory of optimization. Interest in mathematical inequalities for convex and generalized convex functions has been growing exponentially, and research in this respect has had a significant impact on modern analysis [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. For s > 0 and a convex subset B of a real linear space S, a function Ŵ : B → R is said to be s-convex if the inequality.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
