Resumen de Generalization of Some Bounds containing Entropies on Time Scales
Muhammad Bilal, Khuram Ali Khan, Ammara Nosheen, Josip Pecaric
In this paper, weighted Jensen’s inequality for diamond integrals is utilized to get some new inequalities containing entropies. Shanon entropy, triangular discrimination, Jeffreys distance, Bhattacharyya coefficient, Hellinger discrimination and Rényi entropy are introduced and their bounds are derived using diamond–integral formalism. We discussed the classical, discrete and q-analogue of obtained results by restricting the time scale to R, hZ for h > 0 and qN0 for q > 1. For different divergence measures, the entropic bounds are also deduced. Furthermore, resultant inequalities are also discussed considering the Zipf law and the Zipf–Mandelbrot law to establish some new inequalities for isolated points. The new established results are the generalizations of results proved in Ansari et al. (J Inequal Appl 2021:1–21, 2021), Horváth et al. (Bull Malays Math Sci Soc 42:933-946, 2019), Mati´c, Pearce and Peˇcari´c (Shannon’s and related inequalities in information theory. Survey on classical inequalities, Springer, Dordrech, 2000).
