New advances in fixed point theory for contractive mappings on composed $ S $-metric spaces

Nizar Souayah; Nizar Souayah

doi:10.3934/math.2026533

AIMS Mathematics

2026, Volume 11, Issue 5: 12961-12976. doi: 10.3934/math.2026533

Previous Article Next Article

Research article Special Issues

New advances in fixed point theory for contractive mappings on composed $ S $-metric spaces

Nizar Souayah ^,

Computer Science and Engineering Department, College of Applied Studies, King Saud University Riyadh 11437, Saudi Arabia

Received: 01 April 2026 Revised: 26 April 2026 Accepted: 30 April 2026 Published: 11 May 2026
MSC : 54H25, 47H10

Motivated by recent developments of Kil et al., who proposed a new class of composed $ S $-metric type spaces extending the notion of controlled $ S $-metric spaces, this paper investigated fixed point phenomena within this broader setting. We derived existence and uniqueness theorems for fixed points corresponding to various contractive conditions by making essential use of the structural features of the proposed framework. The presented theorems encompassed and extended a number of well-established results in the existing literature. To demonstrate the practical relevance of the theory, a concrete example was included, illustrating the effectiveness of composed $ S $-metric spaces in addressing the solvability of $ n $th-degree polynomial equations.
- composed $ S $-metric spaces,
- fixed point theory,
- $ S $-metric spaces,
- polynomial equations
Citation: Nizar Souayah. New advances in fixed point theory for contractive mappings on composed $ S $-metric spaces[J]. AIMS Mathematics, 2026, 11(5): 12961-12976. doi: 10.3934/math.2026533

Related Papers:

Abstract

Motivated by recent developments of Kil et al., who proposed a new class of composed $ S $-metric type spaces extending the notion of controlled $ S $-metric spaces, this paper investigated fixed point phenomena within this broader setting. We derived existence and uniqueness theorems for fixed points corresponding to various contractive conditions by making essential use of the structural features of the proposed framework. The presented theorems encompassed and extended a number of well-established results in the existing literature. To demonstrate the practical relevance of the theory, a concrete example was included, illustrating the effectiveness of composed $ S $-metric spaces in addressing the solvability of $ n $th-degree polynomial equations.

References

[1]	J. Li, C. Li, N. C. Wong, J. C. Yao, Recent development in fixed-point theory, optimization, and their applications, Abstr. Appl. Anal., 2014 (2014), 293463. http://dx.doi.org/10.1155/2014/293463 doi: 10.1155/2014/293463
[2]	S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math., 3 (1922), 133–181.
[3]	S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in $S$-metric spaces, Mat. Vestn, 64 (2012), 258–266.
[4]	M. Shahraki, S. Sedghi, S. M. A. Aleomraninejad, Z. D. Mitrović, Some fixed point results on $S$-metric spaces, Acta U. Sapientiae-Ma., 12 (2020), 347–357. https://doi.org/10.2478/ausm-2020-0024 doi: 10.2478/ausm-2020-0024
[5]	G. S. Saluja, H. K. Nashine, R. Jain, R. W. Ibrahim, H. A. Nabwey, Common fixed point theorems on $S$-metric spaces for integral type contractions involving rational terms and application to fractional integral equation, J. Funct. Space., 2024 (2024), 5108481. https://doi.org/10.1155/2024/5108481 doi: 10.1155/2024/5108481
[6]	N. Taş, N. Y., Özgür, On parametric $S$-metric spaces and fixed-point type theorems for expansive mappings, J. Math., 2016 (2016), 4746732. https://doi.org/10.1155/2016/4746732 doi: 10.1155/2016/4746732
[7]	N. Taş, N. Y. Özgür, Some fixed-point results on parametric $N_b$-metric spaces, Commun. Korean Math. S., 33 (2018), 943–960.
[8]	N. Souayah, N. Mlaiki, A fixed point theorem in $S_b$-metric sapces, J. Math. Comput. Sci., 16 (2016), 131–139. https://doi.org/10.22436/jmcs.016.02.01 doi: 10.22436/jmcs.016.02.01
[9]	N. Mlaiki, The extended $S_b$-metric spaces, J. Math. Anal., 9 (2018), 124–135.
[10]	N. Mani, S. Beniwal, R. Shukla, M. Pingale, Fixed point theory in extended parametric $S_b$-metric spaces and its applications, Symmetry, 15 (2023), 2136. https://doi.org/10.3390/sym15122136 doi: 10.3390/sym15122136
[11]	Z. Mustafa, R. J. Shahkoohi, V. Parvaneh, Z. Kadelburg, M. M. M. Jaradat, Ordered $S_p$-metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems, Fixed Point Theory A., 2019 (2019), 16. https://doi.org/10.1186/s13663-019-0666-3 doi: 10.1186/s13663-019-0666-3
[12]	N. E. Yazici, O. Ege, N. Mlaiki, A. Mukheimer, Controlled S-metric-type spaces and applications to fractional integrals, Symmetry, 15 (2023), 1100. https://doi.org/10.3390/sym15051100 doi: 10.3390/sym15051100
[13]	N. Mlaiki, N. Y. Özgür, N. Taş, New fixed-point theorems on an S-metric space via simulation functions, Mathematics, 7 (2019), 583. https://doi.org/10.3390/math7070583 doi: 10.3390/math7070583
[14]	C. J. Kil, J. C. Choe, U. R. Rim, Fixed point results for nonlinear F-contractions in composed S-metric spaces, J. Funct. Space., 2025 (2025), 1933779. https://doi.org/10.1155/jofs/1933779 doi: 10.1155/jofs/1933779
[15]	M. Younisa, , H. Ahmadb, F. Asmata, M. $\ddot{O}$zt$\ddot{u}$rk, Analyzing Helmholtz phenomena for mixed boundary values via graphically controlled contractions, Math. Model. Anal., 30 (2025), 342–361. https://doi.org/10.3846/mma.2025.22546 doi: 10.3846/mma.2025.22546

Reader Comments

Your name:*

Email:*
© 2026 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)