TITLE:
Dynamic Inequalities for Convex Functions Harmonized on Time Scales
AUTHORS:
Muhammad Jibril Shahab Sahir
KEYWORDS:
Delta, Nabla and Diamond-α Time Scales, Fractional Integral Inequalities
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.12,
December
28,
2017
ABSTRACT: We present here some general fractional Schl?milch’s
type and Rogers-H?lder’s
type dynamic inequalities for convex functions harmonized on time scales. First
we present general fractional Schl?milch’s type dynamic inequalities and
generalize it for convex functions of several variables by using Bernoulli’s
inequality, generalized Jensen’s inequality and Fubini’s theorem on diamond-α calculus. To conclude
our main results, we present general fractional Rogers-H?lder’s type dynamic
inequalities for convex functions by using general fractional Schl?milch’s type
dynamic inequality on diamond-α calculus for pi>1 with .