Dynamic Inequalities for Convex Functions Harmonized on Time Scales

摘要

style="font-size:10.0pt;font-family:;" "="">We present here some general fractional Schl style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">?milch’s type an style="font-size:10.0pt;font-family:;" "="">d Rogers-H style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">?lder’s type dynamic inequalities for convex functions harmonized on time scales. First we present general fractional Schl style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">?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- style="font-size:10.0pt;font-family:;" "="">α style="font-size:10.0pt;font-family:;" "=""> style="font-size:10.0pt;font-family:;" "="">calculus. To conclude our main results, we present general fractional Rogers-H style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">?lder’s type dynamic inequalities for convex functions by using general fractional Schl style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">?milch’s type dynamic inequality on diamond- style="font-size:10.0pt;font-family:;" "="">α style="font-size:10.0pt;font-family:;" "=""> style="font-size:10.0pt;font-family:;" "="">calculus for p_i style="color:#333333;font-family:" font-size:13px;text-align:center;white-space:normal;background-color:#ffffff;"=""1 with src="Edit_13da77b1-ab27-448b-a8c0-152b39deb7af.bmp" alt="" />.