On Zipf-Mandelbrot entropy and $3$-convex functions

@article{Khalid2019OnZE,
  title={On Zipf-Mandelbrot entropy and \$3\$-convex functions},
  author={Sadia Khalid and Đ. Pe{\vc}ari{\'c} and Josip E. Pe{\vc}ari{\'c}},
  journal={Advances in Operator Theory},
  year={2019}
}
In this paper, we present some interesting results related to the bounds of Zipf–Mandelbrot entropy and the 3-convexity of the function. Further, we define linear functionals as the nonnegative differences of the obtained inequalities and we present mean value theorems for the linear functionals. Finally, we discuss the n-exponential convexity and the log-convexity of the functions associated with the linear functionals. 

Refinements of some Hardy–Littlewood–Pólya type inequalities via Green’s functions and Fink’s identity and related results

In this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r -convex functions. We

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