On some metric inequalities and applications. (English) Zbl 1452.26018
Summary: We derive a new inequality in metric spaces and provide its geometric interpretation. Some applications of our result are given, including metric inequalities in Lebesgue spaces, matrices inequalities, multiplicative metric inequalities, and partial metric inequalities. Our main result is a generalization of that obtained by S. S. Dragomir and A. C. Goşa [J. Indones. Math. Soc. 11, No. 1, 33–38 (2005; Zbl 1069.54507)].
MSC:
| 26D15 | Inequalities for sums, series and integrals |
Citations:
Zbl 1069.54507References:
| [1] | Dragomir, S. S.; Gosa, A. C., An inequality in metric spaces, Journal of The Indonesian Mathematical Society, 11, 1, 33-38 (2005) · Zbl 1069.54507 |
| [2] | Giles, J. R., Introduction to the Analysis of Metric Spaces (1987), Cambridge: Cambridge University Press, Cambridge · Zbl 0645.46001 |
| [3] | Castillo, R. E.; Rafeiro, H., An Introductory Course in Lebesgue Spaces. CMS Books in Mathematics (2016), Berlin: Springer, Berlin · Zbl 1352.46003 · doi:10.1007/978-3-319-30034-4 |
| [4] | Bellman, R., Introduction to Matrix Analysis (1974), New York, NY, USA: McGraw-Hill, New York, NY, USA · Zbl 0124.01001 |
| [5] | Bhatia, R., Matrix Analysis (1997), New York, NY, USA: Springer, New York, NY, USA · doi:10.1007/978-1-4612-0653-8 |
| [6] | Bashirov, A. E.; Kurpınar, E. M.; Özyapıcı, A., Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 337, 1, 36-48 (2008) · Zbl 1129.26007 · doi:10.1016/j.jmaa.2007.03.081 |
| [7] | Ćirić, L.; Samet, B.; Aydi, H.; Vetro, C., Common fixed points of generalized contractions on partial metric spaces and an application, Applied Mathematics and Computation, 218, 6, 2398-2406 (2011) · Zbl 1244.54090 · doi:10.1016/j.amc.2011.07.005 |
| [8] | Karapinar, E.; Agarwal, R. P.; Aydi, H., Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6, 11, 256 (2018) · Zbl 1469.54127 · doi:10.3390/math6110256 |
| [9] | Matthews, S. G., Partial metric topology, Annals of the New York Academy of Sciences, 728, 183-197 (1994) · Zbl 0911.54025 |
| [10] | Vetro, C.; Vetro, F., Common fixed points of mappings satisfying implicit relations in partial metric spaces, Journal of Nonlinear Sciences and Applications, 6, 3, 152-161 (2013) · Zbl 1432.54086 · doi:10.22436/jnsa.006.03.01 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
