Generalization and Extension of Liu,H. and Xu,S. and, Jiandong Wang Results in Cone Metric Spaces Over Banach Algebras for Generalized Lipschitz Conditions
Digital Object Identifier:
10.58578/ajstea.v2i3.2858
Viewed : 38 times
Downloaded : 28 times
Please do not hesitate to contact us if you would like to obtain more information about the submission process or if you have further questions.
Abstract
This article aims to present and establish some fixed-point results for a mapping satisfying generalized Lipschitz conditions and appealing to the normality of the cone. Our results extend and generalize several known results from the existing literature.
Citation Metrics:
Downloads
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
Banach S. (1922). Sure less operations dans les ensembles abstraits et leur application aux equations integrals, Found. Math.3 (1), 133-181. http://eudml.org/doc/213289
Huang and Zhang. (2007). Cone metric spaces and fixed point theorems of contractive Mappings, J. Math. Anal. Appl. 332, 1468-1476. https://doi.org/10.1016/.jmaa.2005.03.087.
Rezapour, Sh. and Hamlbarani, R. (2008). Some notes on the paper-“Cone metric spaces and fixed point theorems of contractive mapping” J.of Math. Anal. Appl.345(2), 719-724. doi:10.1016/j.jmaa.2008.04.049.
Liu,H. and Xu,S.. (2013). Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mapping, Fixed point theory and applications, 2013:320. https://doi.org/10.1186/1687-1812-2013-320.
Shaoyuan Xu and Stojan Radenovic. (2014). Fixed point theorems of generalized Lipschitz mapping on cone metric spaces over Banach algebras without assumption of normality, Fixed point theory and applications, 2014:102. https://doi.org/10.1186/1687-1812-2014-102.
Huaping Huang and Stojan Rdenovics. (2015). Common fixed point theorems of Generalized Lipschitz Mapping in cone metric spaces over Banach algebras, Applied mathematics and information Sciences, 9(6), 2983-2990. DOI:10.12785/amis/090626
Qi yan, Jiandong Yin and Tao Wang. (2016). Fixed point and common fixed point theorems on ordered cone metric spaces over Banach algebra, J. of nonlinear Sci. and appl. 9, 1581-1589. doi.org/10.22436/jnsa.009.04.15.
Cho, Seong-Hoon. (2018). Fixed point theorems in complete cone metric spaces over Banach algebra, Hindawi journal of function spaces, vol.2018, Article ID9395057, 8 pages. https://doi.org/10.1155/2018/9395057
Yan Han and Shaoyuan Xu. (2018). Some new theorems on c- distance without continuity in cone metric spaces over Banach algebras, Hindawij. of function Spaces, vol. 2018, Article Id7463435, 10 Pages. doi.org/10.1155/2018/7463435.
Huaping,H., Stojan Radenovic and Tatjana Dosenovic. (2015). Some common fixed point theorems on c- distance in cone meteic spaces over Banch algebras, 14(2), 180-193. https://www.researchgate.net/publication/317014722.
Ahmad,A. Mitrovic, Z.D.and Salinke, J.N. (2017) On some open problems in cone metric space over Banach algebra, J.of linear and Topological algebra, vol. 6(4), 261-267.
Sastri, K.P.R. Naidu,A.G. and Bakeshaie, T. (2012). Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. Math. Sci. and Engg. Appl. 6, 129-136.
Rudin, W. (1991). S Functional analysis, Mc Graw-Hill, New York,NY, USA,2nd edition.
