Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels
Christopher S. Goodrich, Jagan Mohan Jonnalagadda, Benjamin Lyons
Abstract
We consider positivity, monotonicity, and convexity results for discrete fractional operators with exponential kernels. Our results cover both the sequential and nonsequential cases, and we demonstrate both similarities and dissimilarities between the exponential kernel case and fractional differences with other types of kernels. This shows that the qualitative information gleaned in the exponential kernel case is not precisely the same as in other cases.
Topics & Concepts
MathematicsConvexityMonotonic functionExponential functionKernel (algebra)Applied mathematicsNabla symbolExponential growthPure mathematicsMathematical analysisEconomicsQuantum mechanicsFinancial economicsPhysicsOmegaNonlinear Differential Equations AnalysisMathematical Inequalities and ApplicationsDifferential Equations and Boundary Problems