Some new integral inequalities for Lipschitzian functions
DOI:
https://doi.org/10.11121/ijocta.01.2018.00565Keywords:
Integral inequalities, Lipschitzian function, Hermite-Hadamard inequality, Integral meansAbstract
This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given.
Downloads
References
Hadamard J. (1893). Étude sur les propriétés des fonctions entiéres et en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171–215
İşcan, İ. (2014). Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6), 935–942.
Kilbas, A.A. Srivastava, H.M. and Trujillo, J. (2006). Theory and applications of fractional differential equations, Elsevier, Amsterdam.
Roberts, A.W. and Varberg, D.E. (1973) Convex Functions. Academic Press, 300pp, New York.
Dragomir, S.S. Cho, Y.J. and Kim, S.S. (2000). Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501.
Hwang, S.R. Hsu, K.C. and Tseng, K.L. (2013). Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, Journal of Mathematical Analysis and Applications, vol. 405, no. 2, 546-554.
İşcan, İ. (2014). New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals, International Journal of Analysis, volume 2014, Article ID 353924, 8 pages.
İşcan, İ. (2016). Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1), 77-87.
Downloads
Published
How to Cite
Issue
Section
License
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.
