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Abstract We prove that a class of convexity-type results for sequential fractional delta differences is sharp. More precisely, we consider the sequential fractional delta difference map , for , where… Click to show full abstract
Abstract We prove that a class of convexity-type results for sequential fractional delta differences is sharp. More precisely, we consider the sequential fractional delta difference map , for , where , , and . We demonstrate that , for , together with the auxiliary conditions , , and are sufficient to guarantee that f is a convex map on all of , provided that the pair lives in a specified subregion of the parameter space . Finally, we demonstrate that outside of this specified region the convexity-type result may fail to hold, and so, demonstrate, in this sense, the sharpness of the convexity-type result.
Journal Title: Journal of Difference Equations and Applications
Year Published: 2017
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