On Zipf-Mandelbrot entropy and 3-convex functions the
n-exponential convexity and the log-
convexity of the functions associated with the linear
On Shannon and Zipf–Mandelbrot entropies and related results construct new family of
exponentially convex functions and Cauchy-type means. © 2019, The Author(s).
GENERALIZATION OF MAJORIZATION THEOREM-II deduced from our generalized results by using the family of (
n + 1)-
convex functions at a point. We give
GENERALIZED STEFFENSEN-TYPE INEQUALITIES BY ABEL-GONTSCHAROFF POLYNOMIAL, we present mean value theorems and
n-exponential convexity for these functionals. We also give
FURTHER IMPROVEMENT OF AN EXTENSION OF HOLDER-TYPE INEQUALITY functionals. Moreover, we study the action of related linear functionals on families of
exponentially convex Generalized fractional integral inequalities for exponentially (s, m) -convex functions fractional integral operators for s-
convex, m-
convex, (s, m) -
convex,
exponentially convex,
exponentially s-
convex On (h, g; m)-Convexity and the Hermite-Hadamard Inequality or
exponentially (s, m)-
convex functions. Also, the Hermite-Hadamard inequality for an (h, g; m)
convex function
Generalization of cyclic refinements of Jensen’s inequality by Fink’s identity of the linear functionals obtained from these identities utilizing the theory of inequalities for
n-convex The punishing factors for convex pairs are 2n-1 with the set A(Ω, ∏) of functions f : Ω → ∏ holomorphic on Ω and we prove estimates for |f(
n)(z)|, f ∈ A(Ω, Ω