Strong b-Metric Spaces and Common Fixed Points

Hakima Bouhadjera; Yousra Nour Djihane Rachedi

doi:10.2478/gm-2025-0005

.blurhash-client-img { display: none !important; }

Strong b-Metric Spaces and Common Fixed Points

General Mathematics

Volume 33 (2025): Issue 1 (June 2025)

By: Hakima Bouhadjera and Yousra Nour Djihane Rachedi

Open Access

|Apr 2026

Abstract

This contribution’s aim is to find unique common fixed points using our concept of occasionally weakly biased mappings of type (𝔸), in complete strong b-metric spaces, and by minimal conditions. To convince the readers of the validity and pertinently of our results, we provided for each theorem its suitable example. Our theorems improve some existing results in metric as well as strong b-metric spaces.

References

M. Aslantaş, Best proximity point results on strong b -metric spaces, J. New Theory, vol. 34, 2021, 28–36.
Search in Google Scholar Back to article
I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Func. Anal. Gos. Ped. Inst. Ul’yanowsk, vol. 30, 1989, 26–37.
Search in Google Scholar Back to article
H. Bouhadjera, Fixed points for occasionally weakly biased mappings of type (𝒜), Math. Morav., vol. 26, no. 1, 2022, 113–122.
Search in Google Scholar Back to article
H. Bouhadjera, On common fixed point theorems for three and four self mappings satisfying contractive conditions, Acta Univ. Palack. Olomuc., Fac. Rer. Natur., Math., vol. 49, no. 1, 2010, 25–31.
Search in Google Scholar Back to article
H. Bouhadjera, Fixed points of occasionally weakly compatible maps satisfying general contractive conditions of integral type, Math. Morav., vol. 15, no. 1, 2011, 25–29.
Search in Google Scholar Back to article
H. Bouhadjera, General common fixed point theorems for occasionally weakly compatible maps, Math. Sci., vol. 3, no. 3, 2009, 263–272.
Search in Google Scholar Back to article
H. Bouhadjera, On unique common fixed point theorems for three and four self mappings, Filomat, vol. 23, no. 3, 2009, 115–123.
Search in Google Scholar Back to article
H. Bouhadjera, Some common fixed point theorems for occasionally weakly compatible mappings satisfying implicit relation and contractive modulus, Fasciculi Mathematici, vol. 51, 2013, 1–8.
Search in Google Scholar Back to article
H. Bouhadjera, H. Z. Alzumi, W. Shammakh, S. M. Ali, M. S. Abdo, Unique common fixed points for occasionally weakly based maps of type (A) in b- metric-like spaces, J. Funct. Spaces, Volume 2023, Article ID 3937224, 9 pages, https://doi.org/10.1155/2023/3937224
Search in Google Scholar Back to article
H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for pairs of subcompatible maps, arXiv:0906.3159v1 [Math.FA] 17 Jun 2009.
Search in Google Scholar Back to article
H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible maps, arXiv:0812.3734v2 [Math.FA] 17 Jun 2009.
Search in Google Scholar Back to article
H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for occasionally weakly compatible maps, HAL Id: hal-00273238 https://hal.science/hal-00273238v3, Preprint submitted on 17 Jun 2009.
Search in Google Scholar Back to article
H. Bouhadjera, A. Djoudi, General common fixed point theorems for weakly compatible maps, Gen. Math., vol. 16, no. 2, 2008, 95–107.
Search in Google Scholar Back to article
H. Bouhadjera, A. Djoudi, Common fixed point theorems for subcompatible D-maps of integral type, Gen. Math., vol. 18, no. 4, 2010, 163–174.
Search in Google Scholar Back to article
H. Bouhadjera, A. Djoudi, Common fixed point theorems for pairs of single and multivalued D-maps satisfying an integral type, Ann. Math. Inform., vol. 35, 2008, 43–59.
Search in Google Scholar Back to article
H. Bouhadjera, A. Djoudi, Common fixed point theorems for single and setvalued maps, An. Univ. Oradea Fasc. Mat., vol. 15, 2008, 109–127.
Search in Google Scholar Back to article
S. Czerwik, Contraction mappings in b -metric spaces, Acta Math. Inform. Univ. Ostrav., vol. 1, no. 1, 1993, 5–11.
Search in Google Scholar Back to article
H. Doan, A new type of Kannan ’ s fixed point theorem in strong b -metric spaces, AIMS Mathematics, vol. 6, no. 7, 2021, 7895–908. DOI:10.3934/math.2021458
Search in Google Scholar Back to article
W. Kirk, N. Shahzad, Fixed point theory in distance spaces, Switzerland: Springer, 2014, http://dx.doi.org/10.1007/978-3-319-10927-5
Search in Google Scholar Back to article
E. Qudah, A. Talafhah, Strong b -metric spaces and fixed point theorems, Nonlinear Funct. Anal. Appl., vol. 29, no. 4, 2024, 991–1006.
Search in Google Scholar Back to article
A. Tassaddiq, S. Kanwal, S. Perveen, R. Srivastava, Fixed points of single-valued and multi-valued mappings in sb-metric spaces, J. Inequal. Appl., vol. 85, 2022, https://doi.org/10.1186/s13660-022-02814-z
Search in Google Scholar Back to article
T. Van An, N. Van Dung, Answers to Kirk-Shahzad ’ s questions on strong b- metric spaces, arXiv:1503.08126v2 [Math.GN] 2 Apr 2015.
Search in Google Scholar Back to article
P. Wang, F. He, X. Liu, Answers to questions on Kannan ’ s fixed point theorem in strong b -metric spaces, AIMS Mathematics, vol. 9, no. 2, 2024, 3671–3684. DOI: 10.3934/math.2024180
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/gm-2025-0005 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023

Journal RSS Feed

Language: English

Page range: 64 - 76

Submitted on: Aug 2, 2025

Accepted on: Aug 20, 2025

Published on: Apr 8, 2026

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Standard metric spaces,

b-metric spaces,

strong b-metric spaces,

occasionally weakly biased mappings of type (𝔸),

unique common fixed points

Related subjects:

Mathematics,

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics,

Applied mathematics

© 2026 Hakima Bouhadjera, Yousra Nour Djihane Rachedi, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 1 (June 2025)