Fixed Point and Best Proximity Point Results in PIV-S-Metric Spaces

Mohammad Asim; Mohammad Imdad

doi:10.2478/amsil-2024-0014

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Fixed Point and Best Proximity Point Results in PIV-S-Metric Spaces

Annales Mathematicae Silesianae

Volume 39 (2025): Issue 1 (March 2025)

By: Mohammad Asim and Mohammad Imdad

Open Access

|Jun 2024

Abstract

This paper presents the concept of a partial idempotent valued S-metric space, abbreviated as PIV-S-metric space, as a generalization of both the PIV-metric space and S-metric space. The study utilizes this new framework to establish a fixed point theorem and a best proximity point theorem. Additionally, the paper proves the existence and uniqueness of the best proximity point within this context. Several illustrative examples are provided to demonstrate the practical applications of the main findings.

References

M.S. Asil, S. Sedghi, and Z.D. Mitrović, Partial S-metric spaces and coincidence points, Filomat 33 (2019), no. 14, 4613–4626.
Search in Google Scholar Back to article
M. Asim, M. Imdad, and S. Radenović, Fixed point results in extended rectangular b-metric spaces with an application, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), no. 2, 43–50.
Search in Google Scholar Back to article
M. Asim, A.R. Khan, and M. Imdad, Fixed point results in partial symmetric spaces with an application, Axioms 8 (2019), no. 1, 13, 15 pp.
Search in Google Scholar Back to article
M. Asim, A.R. Khan, and M. Imdad, Rectangular Mb-metric spaces and fixed point results, J. Math. Anal. 10 (2019), no. 1, 10–18.
Search in Google Scholar Back to article
M. Aslantaş, H. Sahin, and U. Sadullah, Some generalizations for mixed multivalued mappings, Appl. Gen. Topol. 23 (2022), no. 1, 169–178.
Search in Google Scholar Back to article
I.A. Bakhtin, The contraction mapping principle in almost metric space (in Russian), in: A.V. Shtraus (ed.), Functional Analysis, No. 30 (in Russian), Ul'yanovsk. Gos. Ped. Inst., Ul'yanovsk, 1989, pp. 26–37.
Search in Google Scholar Back to article
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
Search in Google Scholar Back to article
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), no. 1–2, 31–37.
Search in Google Scholar Back to article
S. Chandok, D. Kumar, and C. Park, C^∗-algebra-valued partial metric space and fixed point theorems, Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 3, Paper No. 37, 9 pp. DOI: 10.1007/s12044-019-0481-0.
Open DOI Search in Google Scholar Back to article
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.
Search in Google Scholar Back to article
K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234–240.
Search in Google Scholar Back to article
L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468–1476.
Search in Google Scholar Back to article
M. Iranmanesh, S. Radenović, and F. Soleimany, Common fixed point theorems in partial idempotent-valued metric spaces, Fixed Point Theory 22 (2021), no. 1, 241–249.
Search in Google Scholar Back to article
M. Iranmanesh, F. Soleimany, and S. Radenović, Some results on fixed points and best approximation in partial idempotent-valued metric spaces, Scientific Publications of the State University of Novi Pazar Ser. A: Appl. Math. Inform. and Mech. 11 (2019), no. 2, 61–74.
Search in Google Scholar Back to article
T. Kamran, M. Samreen, and Q.U. Ain, A generalization of b-metric space and some fixed point theorems, Mathematics 5 (2017), no. 2, 19, 7 pp.
Search in Google Scholar Back to article
Z. Ma and L. Jiang, C^∗-algebra-valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl. (2015), 2015:222, 12 pp.
Search in Google Scholar Back to article
Z. Ma, L. Jiang, and H. Sun, C^∗-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. (2014), 2014:206, 11 pp.
Search in Google Scholar Back to article
S.G. Matthews, Partial metric topology, in: S. Andima et al. (eds.), Papers on General Topology and Applications, Ann. New York Acad. Sci., 728, New York Academy of Sciences, New York, 1994, pp. 183–197.
Search in Google Scholar Back to article
N. Mlaiki, M. Asim, and M. Imdad, C^∗-algebra valued partial b-metric spaces and fixed point results with an application, Mathematics 8 (2020), no. 8, 1381, 11 pp. DOI: 10.3390/math8081381.
Open DOI Search in Google Scholar Back to article
S. Sedghi, N. Shobe, and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64 (2012), no. 3, 258–266.
Search in Google Scholar Back to article
S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), no. 2, 703–711.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2024-0014 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 46 - 63

Submitted on: Aug 23, 2023

Accepted on: May 10, 2024

Published on: Jun 7, 2024

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

fixed point,

idempotent valued metric space,

idempotent valued S-metric space

Related subjects:

Mathematics,

General mathematics

© 2024 Mohammad Asim, Mohammad Imdad, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 39 (2025): Issue 1 (March 2025)