Unique Fixed-point Theories in Various Mathematical Spaces

Author(s)	AKANKSHA SINGH, Dr. MANISH KUMAR SINGH, Dr. RITA SHUKLA
Country	India
Abstract	In a wide variety of mathematical fields, unique fixed-point theories are vital because they serve as fundamental instruments for the investigation of stability, convergence, and the presence of solutions in a variety of spaces. The purpose of this research is to analyse certain fixed-point theorems in a variety of mathematical situations. Metric spaces, Banach spaces, partially ordered sets, and topological spaces are all examples of settings that fall under this category. In the context of increasingly complex frameworks, such as fuzzy metric spaces and probabilistic spaces, traditional results such as Banach's and Brouwer's Fixed-Point Theorems are investigated in combination with their generalisations and extensions. As a means of ensuring that fixed points are one of a kind, the study places particular focus on the significance of compactness, monotonicity, and contractive mappings. Through considerations of their applications in optimisation, computer mathematics, functional analysis, and differential equations, the theoretical and practical significance of unique fixed-point solutions are brought to the forefront.
Keywords	Unique Fixed-Point, Fixed-Point Theorem, Metric Spaces, Banach Space
Published In	Volume 7, Issue 5, September-October 2025
Published On	2025-10-16
DOI	https://doi.org/10.36948/ijfmr.2025.v07i05.57982

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