Abstract
This paper is devoted to obtain generalized results related to majorization-type inequalities by using well-known Fink’s identity and new types of Green functions, introduced by Mehmood et al. (J. Inequal. Appl. 2017:108, 2017). We give a generalized majorization theorem for the class of n-convex functions. We utilize the Csiszár f-divergence and generalized majorization-type inequalities in providing the corresponding generalizations. As an application, we present the obtained results in terms of Shannon entropy and Kullback–Leibler distance.
Highlights
Majorization is a powerful and useful mathematical tool, which arises frequently in many different areas of research
Let us define some new types of Green functions Gl : [θ1, θ2] × [θ1, θ2] → R, where [θ1, θ2] ⊂ R and l = 2, 3, 4, given by Mehmood et al, which are continuous and convex, by keeping in view the Abel–Gontscharoff Green’s function for the “two-point right focal problem”:
2.1 Majorized results using Fink’s identity First, we present two equivalent statements of majorization inequality between newly defined Green functions and continuous convex functions
Summary
Majorization is a powerful and useful mathematical tool, which arises frequently in many different areas of research. In 2018, Latif et al [27] studied generalized results related to majorization inequality by using Taylor’s polynomial in combination with newly introduced Green functions. Our main goal is obtaining generalized results about majorization by using new Green functions and Fink’s identity.
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