Abstract
We introduce the delta-integral representation of divided difference on arbitrary time scales and utilize it to set criteria for n-convex functions involving delta-derivative on time scales. Consequences of the theory appear in terms of estimates which generalize and extend some important facts in mathematical analysis.
Highlights
Time scale calculus is a well known and rapidly growing theory in mathematical analysis which unifies two distinct well-known mathematical areas named as continuous and discrete analysis
The notion is firstly generalized on an arbitrary time scale in 2008 by Cristian Dinu [8], subsequently a large number of estimation and inequalities for the functions that are convex on time scales are in the continuous state of development, some of them are present in [9, 10]
Higher order convex functions has been discussed on time scales with constant graininess function by H
Summary
Time scale calculus is a well known and rapidly growing theory in mathematical analysis which unifies two distinct well-known mathematical areas named as continuous and discrete analysis. The n-convexity or higher order convexity firstly investigated by Eberhard Hopf [11] in his scholarly thesis. Further it was discussed in different narrations by Popoviciu [12, 13]. Pecaricdiscussed some "Jensen-Type Inequalities on Time Scales" involving real-valued n-convex functions. Higher order convex functions has been discussed on time scales with constant graininess function by H. N-convex functions; delta integrals; Time scales; integral inequalities. We presented some mathematical inequalities as consequences of our main results in the last section
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