A Dislocated Quasi-Normed Space and Its Completeness for A Fixed Point Theorem
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Abstract
A concept of a dislocated quasi-normed space is introduced in this paper which is a spatial case of the concept of a quasi-normed space and related to the notion of a dislocated quasi-metric space. Its relationship with other concepts is given by illustrative examples. The completeness of it defines a dislocated quasi-Banach space that is important to our results with respect to a fixed-point theorem. Also, a quasi-contraction mapping is introduced, in which, Lipchitz constant depends on a constant of dislocated quasi-normed space, and then a Banach contraction principle theorem in a dislocated quasi-Banach space is studied with some important results.
Received 18/12/2022
Revised 07/07/2023
Accepted 09/07/2023
Published Online First 20/11/2023
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References
Qadri H, Mahmood Q. On Moduli and Constants Quasi-Banach Space. J Math Sci. 2018; 2(1): 122-133. http://dx.doi.org/10.30538/oms2018.0022
Al-Saphory RAM, Jasim M. Quasi-Compactness in Quasi-Banach Spaces l_p, for 0< p <1. J. Adv Math. 2013; 4(1): 326-342. https://doi.org/10.13140/RG.2.1.2666.9602
Rano G, Bag T. Quasi-Metric Space and Fixed Point Theorems. Int J Math Sci Computing. 2013; 3(2): 27-31. https://api.semanticscholar.org/CorpusID:208509744
Damene M, Koyas K, Gebregiorgis S. Coupled coincidence and coupled common fixed point theorem in dislocated quasi metric space. Eng Appl Sci Lett. 2020; 3(4): 11-18. https://doi.org/10.30538/psrp-easl2020.0047
Alwan AH. On Fixed Points in Orbit in Dislocated Quasi-Metric Spaces. AIP Conf Proc. 2022; 2386(1): 1-6. https://doi.org/10.1063/5.0067438
Sarwar M, Rahman M, Ali G. Some fixed point results in dislocated quasi metric (dq-metric) spaces. J Inequal Appl. 2014; 278(2014): 1–11.
Mahmood Q, Shoaib A, Rasham T, Arshad M. Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces. Mathematics. 2019; 7(1): 1-11. https://doi.org/10.3390/math7010056
Mhanna S, Baiz O, Benaissa H. A Proposal for Revisiting Some Fixed Point Results in Dislocated Quasi-Metric Spaces. J Math Comput Sci. 2021; 11(3): 2746-2754. https://doi.org/10.28919/jmcs/5543
Ansari A, Zoto K. Some Fixed Point Theorems and Cyclic Contractions in Dislocated Quasi-Metric Spaces. Facta Univ Ser Math Inform. 2018; 33(1): 93–108. https://doi.org/10.22190/FUMI1801093A
AL-Jawari NJ. Existence and Controllability Results for Control System in Reflexive Banach Space Using Fixed Point Theorem. Baghdad Sci J. 2020; 17(4): 1283 -1287. https://doi.org/10.21123/bsj.2020.17.4.1283
Abed SS, Abduljabbar MF. Some Results on Normalized Duality Mappings and Approximating Fixed Points in Convex Real Modular Spaces. Baghdad Sci J. 2021; 18(4): 1218-1225. https://doi.org/10.21123/bsj.2021.18.4.1218