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Full-Text Articles in Physical Sciences and Mathematics
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic
Sherman's Inequality And Its Converse For Strongly Convex Functions Withapplications To Generalizedf-Divergences, Slavica Ivelic Bradanovic
Turkish Journal of Mathematics
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f-divergence and derived some reverse relations for …
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Coefficient Bounds And Distortion Theorems For The Certain Analytic Functions, Osman Altintaş, Ni̇zami̇ Mustafa
Turkish Journal of Mathematics
In this paper, we introduce and investigate an analytic function class $% P_{q}(\lambda,A,B)$ that we call the class of $q-$starlike and $q-$convex functions with respect to the parameter $\lambda $. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class.