Research and Innovation Articles
Published 2020-11-20
Keywords
- Synchronous Functions,
- Lipschitzian functions,
- Chebyshev inequality,
- Cauchy-Bunyakovsky-Schwarz inequality
How to Cite
Dragomir, S. S. (2020). Inequalities for D−Synchronous Functions and Related Functionals. Revista Integración, Temas De matemáticas, 38(2), 119–132. https://doi.org/10.18273/revint.v38n2-2020005
Copyright (c) 2020 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
We introduce in this paper the concept of quadruple D−synchronous functions which generalizes the concept of a pair of synchronous functions, we establish an inequality similar to Chebyshev inequality and we also provide some Cauchy-Bunyakovsky-Schwarz type inequalities for a functional associated with this quadruple. Some applications for univariate functions of real variable are given. Discrete inequalities are also stated.
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References
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Dragomir S.S., “A counterpart of Schwarz’s inequality in inner product spaces”. arXiv: math/0305373.
Dragomir S.S., “A generalization of the Cassels and Greub-Reinboldt inequalities in inner product spaces”. arXiv: math/0306352.
Dragomir S.S., Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc, New York, 2005.
Dragomir S.S., “Reverses of Schwarz inequality in inner product spaces with applications”, Math. Nachr. 288 (2015), No. 7, 730-742. doi: 10.1002/mana.201300100.
Izumino S., Mori H. and Seo Y., “On Ozeki’s inequality”, J. Inequal. Appl. 2 (1998), No. 3, 235-253. doi: 10.1155/S1025583498000149.
Dragomir S.S., “A counterpart of Schwarz’s inequality in inner product spaces”. arXiv: math/0305373.
Dragomir S.S., “A generalization of the Cassels and Greub-Reinboldt inequalities in inner product spaces”. arXiv: math/0306352.
Dragomir S.S., Advances in Inequalities of the Schwarz, Grüss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc, New York, 2005.
Dragomir S.S., “Reverses of Schwarz inequality in inner product spaces with applications”, Math. Nachr. 288 (2015), No. 7, 730-742. doi: 10.1002/mana.201300100.
Izumino S., Mori H. and Seo Y., “On Ozeki’s inequality”, J. Inequal. Appl. 2 (1998), No. 3, 235-253. doi: 10.1155/S1025583498000149.