TY - JOUR
T1 - Milne type inequality and interval orders
AU - Román-Flores, H.
AU - Ayala, V.
AU - Flores-Franulič, A.
N1 - Publisher Copyright:
© 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.
PY - 2021/6
Y1 - 2021/6
N2 - In this paper, we prove some Milne type inequalities for interval-valued functions and, along with it, we explore some connections with other inequalities. More precisely, using the Aumann integral and the Kulisch–Miranker order and including-order on the space of real and compact intervals, we establish some Milne type inequalities for interval-valued functions. Also, using different orders, we obtain some connections with Chebyshev, Cauchy–Schwarz, and Hölder inequality. Finally, some new ideas and results based on submodular measures are explored as well as some examples and applications are presented for illustrating our results.
AB - In this paper, we prove some Milne type inequalities for interval-valued functions and, along with it, we explore some connections with other inequalities. More precisely, using the Aumann integral and the Kulisch–Miranker order and including-order on the space of real and compact intervals, we establish some Milne type inequalities for interval-valued functions. Also, using different orders, we obtain some connections with Chebyshev, Cauchy–Schwarz, and Hölder inequality. Finally, some new ideas and results based on submodular measures are explored as well as some examples and applications are presented for illustrating our results.
KW - Integral inequalities
KW - Interval orders
KW - Interval-valued functions
KW - Milne’s inequality
UR - https://www.scopus.com/pages/publications/85105232938
U2 - 10.1007/s40314-021-01500-y
DO - 10.1007/s40314-021-01500-y
M3 - Article
AN - SCOPUS:85105232938
SN - 2238-3603
VL - 40
JO - Computational and Applied Mathematics
JF - Computational and Applied Mathematics
IS - 4
M1 - 130
ER -