F. Zhang - Institute of Civil Engineering, Huzhou Vocational \(\&\) Technical College, Huzhou 313000, P. R. China. M. A. Khan - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. S. I. Bradanovic - Faculty of Civil Engineering, Architecture And Geodesy, University of Split, Matice Hrvatske 15, 21000 Split, Croatia. T. Saeed - Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. H. M. K. Khel - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
An interesting approach for deriving interpolating Sherman-type inequalities is utilized in this research work, using Jensen-type inequality for strongly convex functions along with some conditions of majorization. The acquired results are utilized to develop new estimates for strong \(f\)-divergences, a concept related to Csiszar \(f\)-divergences for strongly convex functions. These inequalities allow us to set new limits for frequently utilized divergences, like the Hellinger divergence, Kullback-Leibler divergence, \(\chi^{2}\)-divergence, Jeffreys distance, Bhattacharyya coefficient, and Jensen-Shannon divergence. Additionally, our results yield improved estimates for Shannon entropy.
F. Zhang, M. A. Khan, S. I. Bradanovic, T. Saeed, H. M. K. Khel, Interpolating Sherman-type inequalities and refined bounds for strong \(f\)-divergences, Journal of Mathematics and Computer Science, 40 (2026), no. 2, 209--225
Zhang F., Khan M. A., Bradanovic S. I., Saeed T., Khel H. M. K., Interpolating Sherman-type inequalities and refined bounds for strong \(f\)-divergences. J Math Comput SCI-JM. (2026); 40(2):209--225
Zhang, F., Khan, M. A., Bradanovic, S. I., Saeed, T., Khel, H. M. K.. "Interpolating Sherman-type inequalities and refined bounds for strong \(f\)-divergences." Journal of Mathematics and Computer Science, 40, no. 2 (2026): 209--225
