Lipschitz isomorphism and fixed point theorem for normed groups

References

• Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3(1), 133–21. https://doi.org/10.4064/fm-3-1-133-181
   Google Scholar
• Batagelj, V. (1995). Norms and distances over finite groups. Journal of Combinatorics, Information & System Sciences, 20(1–4), 243–252. http://vlado.fmf.uni-lj.si/pub/preprint/GroupDis.pdf
   Google Scholar
• Bingham, N., & Ostaszewski, A. (2010). Normed versus topological groups: Dichotomy and duality. Dissertationes Mathematicae, 472, 1–138. https://doi.org/10.4064/dm472-0-1
   Google Scholar
• Birkhoff, G. (1936). A note on topological groups. Compositio Mathematica, 3, 427–430. http://www.numdam.org/article/CM_1936__3__427_0.pdf
   Google Scholar
• Bökamp, T. (1994). Extending norms on groups. Note di Matematica, 14(2), 217–227. http://siba-ese.unisalento.it/index.php/notemat/article/view/932
   Google Scholar
• Debnath, P. (2020). Set-valued Meir–Keeler, Geraghty and Edelstein type fixed point results in b-metric spaces. Rendiconti del Circolo Matematico di Palermo, (2), 1–10. http://siba-ese.unisalento.it/index.php/notemat/article/view/932
   Google Scholar
• Debnath, P., Choudhury, B. S., & Neog, M. (2016). Fixed set of set valued mappings with set valued domain in terms of start set on a metric space with a graph. Fixed Point Theory and Applications, 2017(1), 5. https://doi.org/10.1186/s13663-017-0598-8
   Google Scholar
• Debnath, P., Neog, M., & Radenović, S. (2020). Set valued Reich type G-contractions in a complete metric space with graph. Rendiconti del Circolo Matematico di Palermo Series 2, 69(3), 917–924. https://doi.org/10.1007/s12215-019-00446-9
   Web of Science ®Google Scholar
• Debnath, P., & Sen, M. D. L. (2020). Contractive inequalities for some asymptotically regular set-valued mappings and their fixed points. Symmetry, 12(3), 411. https://doi.org/10.3390/sym12030411
   Google Scholar
• Debnath, P., & Srivastava, H. M. (2020). New extensions of Kannan’s and Reich’s fixed point theorems for multivalued maps using Wardowski’s technique with application to integral equations. Symmetry, 12(7), 1090. https://doi.org/10.3390/sym12071090
   Google Scholar
• Debnath, P., & Srivastava, H. M. (2020). Global optimization and common best proximity points for some multivalued contractive pairs of mappings. Axioms, 9(3), 102. https://doi.org/10.3390/axioms9030102
   Web of Science ®Google Scholar
• Hussain, N., Parvaneh, V., Samet, B., & Vetro, C. (2015). Some fixed point theorems for generalized contractive mappings in complete metric spaces. Fixed Point Theory and Applications, 1(1), 185. https://doi.org/10.1186/s13663-015-0433-z
   Google Scholar
• Jain, S., Jain, S., & Jain, L. B. (2012). On Banach contraction principle in a cone metric space. Journal of Nonlinear Sciences and Applications, 5(4), 252–258. https://doi.org/10.22436/jnsa.005.04.01
   Google Scholar
• Jleli, M., & Samet, B. (2014). A new generalization of the Banach contraction principle. Journal of Inequalities and Applications, 2014(1), 38. https://doi.org/10.1186/1029-242X-2014-38
   Google Scholar
• Kakutani, S. (1936). Über die Metrisation der topologischen Gruppen. Proceedings of the Imperial Academy, 12(4), 82–84. https://doi.org/10.3792/pia/1195580206
   Google Scholar
• Klee, V. L. (1952). Invariant metrics in groups (solution of a problem of Banach). Proceedings of the American Mathematical Society, 3(3), 484–487. https://doi.org/10.1090/S0002-9939-1952-0047250-4
   Web of Science ®Google Scholar
• Merryfield, J., Rothschild, B., & Stein, J., Jr. (2002). An application of Ramsey’s theorem to the Banach contraction principle. Proceedings of the American Mathematical Society, 130(4), 927–933. https://doi.org/10.1090/S0002-9939-01-06169-X
   Web of Science ®Google Scholar
• Neog, M., Debnath, P., & Radenovic, S. (2019). New extension of some common fixed point theorems in complete metric spaces. Fixed Point Theory, 20(2), 567–580. https://doi.org/10.24193/fpt-ro.2019.2.37
   Web of Science ®Google Scholar
• Nourouzi, K., & Pourmoslemi, A. (2017). Probabilistic normed groups. Iranian Journal of Fuzzy Systems, 14(1), 99–113. https://doi.org/10.22111/IJFS.2017.3045
   Web of Science ®Google Scholar
• Pata, V. (2011). A fixed point theorem in metric spaces. Journal of Fixed Point Theory and Applications, 10(2), 299–305. https://doi.org/10.1007/s11784-011-0060-1
   Web of Science ®Google Scholar
• Sarfraz, M., & Li, Y. (2019). Norms over Finitely Generated Abelian Group. International Journal of Algebra, 13(8), 431–443. https://doi.org/10.12988/ija.2019.91038
   Google Scholar
• Shatanawi, W., & Nashine, H. K. (2012). A generalization of Banach’s contraction principle for nonlinear contraction in a partial metric space. Journal of Nonlinear Sciences and Applications, 5(1), 37–43. https://doi.org/10.22436/jnsa.005.01.05
   Google Scholar
• Suksumran, T. (2019). Geometry of generated groups with metrics induced by their Cayley color graphs. Analysis and Geometry in Metric Spaces, 7(1), 15–21. https://doi.org/10.1515/agms-2019-0002
   Web of Science ®Google Scholar
• Zorzitto, F. (1985). Discretely normed abelian groups. Aequationes Mathematicae, 29(1), 172–174. https://doi.org/10.1007/BF02189825
   Google Scholar