Measure theoretic generalizations of Jensen's inequality by Fink's identity (CROSBI ID 314693)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Butt, Saad Ihsan ; Rasheed, Tahir ; Pecaric, Đilda ; Pecaric, Josip
engleski
Measure theoretic generalizations of Jensen's inequality by Fink's identity
We generalize integral Jensen’s inequality and its converse for real Stieltjes measure utilizing the theory of n−convex function by employing Fink’s identity. We also give several versions of discrete Jensen’s inequality along with its reverses and its converse for real weights. As an application we give generalized variants of Hermite-Hadamard’s inequality. Also we give applications in information theory by giving new estimations of generalized divergence functional, Shannon and relative entropies. Finally we give connections to Zipf-Mandelbrot and hybrid Zipf- Mandelbrot entropies.
Jensen’s inequality ; n-convex function ; Fink’s identity ; divergence functional ; entropy ; hybrid Zipf-Mandelbrot entropy
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Podaci o izdanju
23 (1)
2022.
131-154
objavljeno
1787-2405
1787-2413
10.18514/MMN.2022.3656
Povezanost rada
Informacijske i komunikacijske znanosti, Interdisciplinarne društvene znanosti, Interdisciplinarne prirodne znanosti, Matematika