Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

Raghavendra Singh Rathore; Rekha Agrawal

doi:doi:10.11648/j.pamj.20241305.11

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Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

Raghavendra Singh Rathore^*

, Rekha Agrawal

Published in Pure and Applied Mathematics Journal (Volume 13, Issue 5)

Received: 28 August 2024 Accepted: 14 September 2024 Published: 29 September 2024

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Abstract

The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.

Published in	Pure and Applied Mathematics Journal (Volume 13, Issue 5)
DOI	10.11648/j.pamj.20241305.11
Page(s)	66-71
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Occasionally Weakly Compatible Maps, M-Fuzzy Metric Space, Tripled Fixed Point

References

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[3]	Berinde V. and Borcut M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Analysis, 74(2011) 4889 - 4897.
[4]	Borcut M. and Berinde V, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218(2012) 5929-5936.
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[11]	M. A. Al-Thagafi, N. Shahzad, Generalized I-nonexpansive selfmaps and invariant approximations, Acta. Math. Sin., 24(2008), pp. 867-876.
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[15]	Roldan A, Martinez J.-Moreno and Roldan C., Tripled fixed point theorem in fuzzy metric spaces and applications, Fixed Point Theory Appl., (2013) 13 pages.
[16]	R. S. Rathore, Rekha Agrawal and R S Chandel, Common Fixed Point Theorem in M-Fuzzy Metric Space for Occasionally Weakly Compatible Mapping Satisfying Integral type Inequality, Advances in Fixed Point Theory, 2021, 11: 3, 1 -11 https://doi.org/10.28919/afpt/5222 ISSN: 1927-6303.
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APA Style

Rathore, R. S., Agrawal, R. (2024). Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure and Applied Mathematics Journal, 13(5), 66-71. https://doi.org/10.11648/j.pamj.20241305.11

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ACS Style

Rathore, R. S.; Agrawal, R. Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure Appl. Math. J. 2024, 13(5), 66-71. doi: 10.11648/j.pamj.20241305.11

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AMA Style

Rathore RS, Agrawal R. Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure Appl Math J. 2024;13(5):66-71. doi: 10.11648/j.pamj.20241305.11

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@article{10.11648/j.pamj.20241305.11,
  author = {Raghavendra Singh Rathore and Rekha Agrawal},
  title = {Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings
},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {5},
  pages = {66-71},
  doi = {10.11648/j.pamj.20241305.11},
  url = {https://doi.org/10.11648/j.pamj.20241305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241305.11},
  abstract = {The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.
},
 year = {2024}
}

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TY  - JOUR
T1  - Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

AU  - Raghavendra Singh Rathore
AU  - Rekha Agrawal
Y1  - 2024/09/29
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241305.11
DO  - 10.11648/j.pamj.20241305.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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EP  - 71
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241305.11
AB  - The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.

VL  - 13
IS  - 5
ER  -

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Author Information

Raghavendra Singh Rathore

Department of Mathematics, Govt Madhav Science College, Vikram University, Ujjain, India

Contact Email

http://orcid.org/0000-0003-0843-0681
Rekha Agrawal

Department of Mathematics, Govt Girls’ Geetanjali College, Barkatullah University, Bhopal, India

Contact Email

http://orcid.org/0009-0000-1639-8672

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Plain Text BibTeX RIS

APA Style

Rathore, R. S., Agrawal, R. (2024). Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure and Applied Mathematics Journal, 13(5), 66-71. https://doi.org/10.11648/j.pamj.20241305.11

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ACS Style

Rathore, R. S.; Agrawal, R. Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure Appl. Math. J. 2024, 13(5), 66-71. doi: 10.11648/j.pamj.20241305.11

Copy | Download

AMA Style

Rathore RS, Agrawal R. Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings. Pure Appl Math J. 2024;13(5):66-71. doi: 10.11648/j.pamj.20241305.11

Copy | Download

@article{10.11648/j.pamj.20241305.11,
  author = {Raghavendra Singh Rathore and Rekha Agrawal},
  title = {Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings
},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {5},
  pages = {66-71},
  doi = {10.11648/j.pamj.20241305.11},
  url = {https://doi.org/10.11648/j.pamj.20241305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241305.11},
  abstract = {The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings

AU  - Raghavendra Singh Rathore
AU  - Rekha Agrawal
Y1  - 2024/09/29
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241305.11
DO  - 10.11648/j.pamj.20241305.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 66
EP  - 71
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241305.11
AB  - The fixed point theorems, which are primarily existential in nature, serve as a fundamental topological toolkit for the qualitative analysis of solutions to both linear and nonlinear equations in various branches of mathematics. Many authors have extended and generalized these results in different ways, particularly in the context of fuzzy metric spaces and fuzzy mappings. Numerous researchers have also proved common fixed point theorems under the condition of compatible mappings for fizzy metric spaces. Coupled common fixed point theorems for fuzzy metric spaces with the condition of weakly compatible mappings were attempted to be proved by many authors. Tripled fixed points have emerged as a significant area of research within fixed point theory. Berinde and Borcut introduced the concept of a tripled fixed point for nonlinear mappings in partially ordered metric spaces. They also established a common fixed point theorem for contractive type mappings in M-fuzzy metric spaces. Later, other authors extended these results for common tripled fixed point theorems in fuzzy metric spaces. In this paper we introduce a new technique for proving some new common tripled fixed point theorems for Occasionally Weakly Compatible Mappings in M-fuzzy metric spaces, a method which is not previously utilized by authors in this field. Additionally, we provide illustrative example to support our findings, which represent an improvement over recent results found in the literature.

VL  - 13
IS  - 5
ER  -

Copy | Download