Complex-valued controlled rectangular metric type spaces and application to linear systems

Fatima M. Azmi; Nabil Mlaiki; Salma Haque; Wasfi Shatanawi; Fatima M. Azmi; Nabil Mlaiki; Salma Haque; Wasfi Shatanawi

doi:10.3934/math.2023848

AIMS Mathematics

2023, Volume 8, Issue 7: 16584-16598. doi: 10.3934/math.2023848

Previous Article Next Article

Research article

Complex-valued controlled rectangular metric type spaces and application to linear systems

1.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 13 March 2023 Revised: 27 April 2023 Accepted: 03 May 2023 Published: 11 May 2023
MSC : 47H10, 54H25

Fixed point theory can be generalized to cover multidisciplinary areas such as computer science; it can also be used for image authentication to ensure secure communication and detect any malicious modifications. In this article, we introduce the notion of complex-valued controlled rectangular metric-type spaces, where we prove fixed point theorems for self-mappings in such spaces. Furthermore, we present several examples and give two applications of our main results: solving linear systems of equations and finding a unique solution for an equation of the form $ f(x) = 0 $.
- complex valued controlled rectangular metric type spaces,
- fixed point,
- linear system of equations
Citation: Fatima M. Azmi, Nabil Mlaiki, Salma Haque, Wasfi Shatanawi. Complex-valued controlled rectangular metric type spaces and application to linear systems[J]. AIMS Mathematics, 2023, 8(7): 16584-16598. doi: 10.3934/math.2023848

Related Papers:

Abstract

Fixed point theory can be generalized to cover multidisciplinary areas such as computer science; it can also be used for image authentication to ensure secure communication and detect any malicious modifications. In this article, we introduce the notion of complex-valued controlled rectangular metric-type spaces, where we prove fixed point theorems for self-mappings in such spaces. Furthermore, we present several examples and give two applications of our main results: solving linear systems of equations and finding a unique solution for an equation of the form $ f(x) = 0 $.

References

[1]	S. Banach, Sur les operations dans les ensembles et leur application aux equation sitegrales, Fund. Math., 3 (1922), 133–181. https://doi.org/10.4064/FM-3-1-133-181 doi: 10.4064/FM-3-1-133-181
[2]	J. A. Gatica, W. A. Kirk, A fixed point theorem for k-set-contractions defined in a cone, Pac. J. Math., 53 (1974), 131–136.
[3]	Z. Zhang, K. Wang, On fixed point theorems of mixed monotone operators and applications, Nonlinear Anal. Theor., 70 (2009), 3279–3284. https://doi.org/10.1016/j.na.2008.04.032 doi: 10.1016/j.na.2008.04.032
[4]	J. Brzdek, M. Piszczek, Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability, J. Fixed Point Theory Appl., 19 (2017), 2441–2448. https://doi.org/10.1007/s11784-017-0441-1 doi: 10.1007/s11784-017-0441-1
[5]	S. Nadler, Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475–488.
[6]	S. Ghaler, 2-metrishche raume und ihre topologische strukture, Math. Nachr., 26 (1963), 115–148. https://doi.org/10.1002/mana.19630260109 doi: 10.1002/mana.19630260109
[7]	I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Func. Anal. Gos. Ped. Inst. Unianowsk, 30 (1989), 26–37.
[8]	S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5–11.
[9]	M. A. Kutbi, E. Karapınar, J. Ahmad, A. Azam, Some fixed point results for multi-valued mappings in b-metric spaces, J. Inequal. Appl., 2014 (2014), 126. https://doi.org/10.1186/1029-242X-2014-126 doi: 10.1186/1029-242X-2014-126
[10]	T. Kamran, M. Samreen, Q. U. Ain, A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5 (2017), 19. https://doi.org/10.3390/math5020019 doi: 10.3390/math5020019
[11]	E. Karapinar, A short survey on the recent fixed point results on b-metric spaces, Constructive Mathematical Analysis, 1 (2018), 15–44. https://doi.org/10.33205/cma.453034 doi: 10.33205/cma.453034
[12]	W. Shatanawi, K. Abodayeh, A. Mukheimer, Some fixed point theorems in extended $b$-metric spaces, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 80 (2018), 71–78.
[13]	R. George, S. Radenovic, P. K. Reshma, S. Shukla, Rectangular $b$-metric space and contraction principles, J. Nonlinear Sci. Appl., 8 (2015), 1005–1013. https://doi.org/10.22436/JNSA.008.06.11 doi: 10.22436/JNSA.008.06.11
[14]	N. Mlaiki, M. Hajji, T. Abdeljawad, A new extension of the rectangular-metric spaces, Adv. Math. Phys., 2020 (2020), 8319584. https://doi.org/10.1155/2020/8319584 doi: 10.1155/2020/8319584
[15]	N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle, Mathematics, 6 (2018), 194. https://doi.org/10.3390/math6100194 doi: 10.3390/math6100194
[16]	T. Abdeljawad, N. Mlaiki, H. Aydi, N. Souayah, Double controlled metric type spaces and some fixed point results, Mathematics, 6 (2018), 320. https://doi.org/10.3390/math6120320 doi: 10.3390/math6120320
[17]	W. Shatanawi, Common fixed points for mappings under contractive conditions of $(\alpha, \beta, \psi)$-admissibility type, Mathematics, 6 (2018), 261. https://doi.org/10.3390/math6110261 doi: 10.3390/math6110261
[18]	N. Y. Özgür, N. Mlaiki, N. Taş, N. Souayah, A new generalization of metric spaces: rectangular M-metric spaces, Math. Sci., 12 (2018), 223–233. https://doi.org/10.1007/s40096-018-0262-4 doi: 10.1007/s40096-018-0262-4
[19]	M. Zhou, N. Saleem, X. L. Liu, N. Ozgur, On two new contractions and discontinuity on fixed points, AIMS Mathematics, 7 (2022), 1628–1663. https://doi.org/10.3934/math.2022095 doi: 10.3934/math.2022095
[20]	A. Latif, R. F. A. Subaie, M. O. Ansari, Fixed points of generalized multi-valued contractive mappings in metric type spaces, J. Nonlinear Var. Anal., 6 (2022), 123–138. https://doi.org/10.23952/jnva.6.2022.1.07 doi: 10.23952/jnva.6.2022.1.07
[21]	E. Karapınar, R. P. Agarwal, S. S. Yesilkaya, C. Wang, Fixed-point results for Meir-Keeler type contractions in partial metric spaces: a survey, Mathematics, 10 (2022), 3109. https://doi.org/10.3390/math10173109 doi: 10.3390/math10173109
[22]	F. M. Azmi, New fixed point results in double controlled metric type spaces with applications, AIMS Mathematics, 8 (2023), 1592–1609. https://doi.org/10.3934/math.2023080 doi: 10.3934/math.2023080
[23]	F. M. Azmi, New contractive mappings and solutions to boundary-value problems in triple controlled metric type spaces, Symmetry, 14 (2022), 2270. https://doi.org/10.3390/sym14112270 doi: 10.3390/sym14112270
[24]	A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex-valued metric spaces, Numer. Func. Anal. Opt., 32 (2011), 243–253.
[25]	K. Rao, P. Swamy, J. Prasad, A common fixed point theorem in complex-valued b-metric spaces, Bulletin of Mathematics and Statistics Research, 1 (2013), 1–8.
[26]	N. Ullah, M. S. Shagari, A. Azam, Fixed point theorems in complex-valued extended $b$-metric spaces, Journal of Pure and Applied Analysis, 5 (2019), 140–163. https://doi.org/10.2478/mjpaa-2019-0011 doi: 10.2478/mjpaa-2019-0011
[27]	M. Abbas, V. Raji, T. Nazir, S. Radenovi, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afr. Mat., 26 (2015), 17–30. https://doi.org/10.1007/s13370-013-0185-z doi: 10.1007/s13370-013-0185-z
[28]	N. Ullah, M. S. Shagari, Fixed point results in complex-valued rectangular extended $b$-metric spaces with applications, Mathematical Analysis and Complex Optimization, 1 (2020), 107–120. https://doi.org/10.29252/maco.1.2.11 doi: 10.29252/maco.1.2.11
[29]	N. Mlaiki, T. Abdeljawad, W. Shatanawi, H. Aydi, Y. Gaba, On complex-valued triple controlled metric spaces and applications, J. Funct. Space., 2021 (2021), 5563456. https://doi.org/10.1155/2021/5563456 doi: 10.1155/2021/5563456
[30]	M. S. Aslam, M. S. R. Chowdhury, L. Guran, M. A. Alqudah, T. Abdeljawad, Fixed point theory in complex valued controlled metric spaces with an application, AIMS Mathematics, 7 (2022), 11879–11904. https://doi.org/10.3934/math.2022663 doi: 10.3934/math.2022663

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)