TY - JOUR
T1 - Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation
AU - Stojiljković, Vuk
AU - Ramaswamy, Rajagopalan
AU - Abdelnaby, Ola A.Ashour
AU - Radenović, Stojan
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - convex set-valued functions
KW - Hermite–Hadamard inequality
KW - Katugampola noninteger integral operators
KW - left–right-(k,h-m)-p-convex set-valued functions
UR - http://www.scopus.com/inward/record.url?scp=85144663524&partnerID=8YFLogxK
U2 - 10.3390/fractalfract6120726
DO - 10.3390/fractalfract6120726
M3 - Article
AN - SCOPUS:85144663524
SN - 2504-3110
VL - 6
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 12
M1 - 726
ER -