Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations
Joint Authors
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-01-03
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The classical Hölder inequality shows an interesting upper bound for Lebesgue integral of the product of two functions.
This paper proposes Hölder type inequalities and reverse Hölder type inequalities for Sugeno integrals under usual multiplication operations for nonincreasing concave or convex functions.
One of the interesting results is that the inequality, (S)∫01f(x)pdμ1/p(S)∫01g(x)qdμ1/q≤p-q/p-p-q+1∨q-p/q-q-p+1(S)∫01f(x)g(x)dμ, where 1
As a special case, we consider Cauchy-Schwarz type inequalities for Sugeno integrals involving nonincreasing concave or convex functions.
Some examples are provided to illustrate the validity of the proposed inequalities.
American Psychological Association (APA)
Hong, Dug Hun& Kim, Jae Duck. 2019. Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations. Advances in Fuzzy Systems،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1118047
Modern Language Association (MLA)
Hong, Dug Hun& Kim, Jae Duck. Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations. Advances in Fuzzy Systems No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1118047
American Medical Association (AMA)
Hong, Dug Hun& Kim, Jae Duck. Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations. Advances in Fuzzy Systems. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1118047
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1118047