Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation
Vuk Stojiljković, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, Stojan Radenović
Abstract
In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results.
Topics & Concepts
MathematicsConvexityHadamard transformConvex functionLogarithmically convex functionConvex setRegular polygonSubderivativeCombinatoricsPure mathematicsFunction (biology)Interval (graph theory)Convex optimizationMathematical analysisGeometryEconomicsBiologyFinancial economicsEvolutionary biologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsOptimization and Variational Analysis