TY - JOUR
T1 - Trapezium-type inequalities for raina’s fractional integrals operator using generalized convex functions
AU - Vivas-Cortez, Miguel
AU - Kashuri, Artion
AU - Hernández Hernández, Jorge E.
N1 - Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2020/6/20
Y1 - 2020/6/20
N2 - The authors have reviewed a wide production of scientific articles dealing with the evolution of the concept of convexity and its various applications, and based on this they have detected the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function. The authors approach this situation by studying the Hermite–Hadamard inequality, establishing a useful identity using Raina’s fractional integral operator in the setting of φ-convex functions, obtaining some integral inequalities connected with the right-hand side of Hermite–Hadamard-type inequalities for Raina’s fractional integrals. Various special cases have been identified.
AB - The authors have reviewed a wide production of scientific articles dealing with the evolution of the concept of convexity and its various applications, and based on this they have detected the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function. The authors approach this situation by studying the Hermite–Hadamard inequality, establishing a useful identity using Raina’s fractional integral operator in the setting of φ-convex functions, obtaining some integral inequalities connected with the right-hand side of Hermite–Hadamard-type inequalities for Raina’s fractional integrals. Various special cases have been identified.
KW - Generalized convexity
KW - Hermite–Hadamard inequality
KW - Hölder inequality
KW - Power mean inequality
KW - Raina’s fractional integral operator
UR - http://www.scopus.com/inward/record.url?scp=85089435555&partnerID=8YFLogxK
U2 - 10.3390/sym12061034
DO - 10.3390/sym12061034
M3 - Article
AN - SCOPUS:85089435555
SN - 2073-8994
VL - 12
SP - 1
EP - 17
JO - Symmetry
JF - Symmetry
IS - 6
M1 - 1034
ER -