New Bounds For Shannon, Relative And Mandelbrot Entropies Via Hermite Interpolating Polynomial (CROSBI ID 256242)
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Podaci o odgovornosti
Butt, Saad Ihsan ; Mehmood, Nasir ; Pečarić, Đilda ; Pečarić, Josip
engleski
New Bounds For Shannon, Relative And Mandelbrot Entropies Via Hermite Interpolating Polynomial
To procure inequalities for divergences between probability distributions, Jensen’s inequality is the key to success. Shannon, Relative and Zipf- Mandelbrot entropies have many applications in many applied sciences, such as, in information theory, biology and economics, etc. We consider discrete and continuous cyclic refinements of Jensen’s inequality and extend them from convex function to higher order convex function by means of different new Green functions by employing Hermite interpolating polynomial whose error term is approximated by Peano’s kernal. As an application of our obtained results, we give new bounds for Shannon, Relative and Zipf-Mandelbrot entropies.
n-convex function ; Hermite interpolating polynomial ; new Green functions ; Shannon entropy ; Relative entropy ; Zipf-Mandelbrot entropy
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Podaci o izdanju
Povezanost rada
Matematika