Research Article
Common Tripled Fixed Point Theorem on M- Fuzzy Metric Space for Occasionally Weakly Compatible Mappings
Raghavendra Singh Rathore*
,
Rekha Agrawal
Issue:
Volume 13, Issue 5, October 2024
Pages:
66-71
Received:
28 August 2024
Accepted:
14 September 2024
Published:
29 September 2024
DOI:
10.11648/j.pamj.20241305.11
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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.
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 s...
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Research Article
A∞-algebra Structure on Connected Multiplicative Operad
Batkam Mbatchou Vane Jacky III*,
Calvin Tcheka
Issue:
Volume 13, Issue 5, October 2024
Pages:
72-78
Received:
2 August 2024
Accepted:
9 September 2024
Published:
29 September 2024
DOI:
10.11648/j.pamj.20241305.12
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Abstract: This work develops the structure of A∞-algebras on operad theory and also the preservation of this structure by a morphism of operads well defined. This structure defined here is motivated by the important role that play certain particular properties such as multiplication and connectivity on the operads. Another key ingredient used to develop this work is the brace operations; which, combined with the properties cited above allowed to better frame the study of this structure. Thus, this paper show explicitly the existence of an A∞-algebra structure on any connected multiplicative operad endowed with its brace operations and that this structure is minimal if the operad is only multiplicative. Furthermore, the paper also shows the existence of an operads morphism from an unital associative operad, Ass to any connected multiplicative operad 𝒪 preserving the structure of A∞-algebras existing on these two operads. And when the operad 𝒪 is just multiplicative then there is rather a morphism of operads from the associative operad, Asto 𝒪 preserving this time the minimal A∞-algebras structure existing on these operads.
Abstract: This work develops the structure of A∞-algebras on operad theory and also the preservation of this structure by a morphism of operads well defined. This structure defined here is motivated by the important role that play certain particular properties such as multiplication and connectivity on the operads. Another key ingredient used to develo...
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