Advanced Fixed-Point Theorems in Partial Metric Spaces under Generalized Contractive Mappings

Author(s)	Ms. Maitreyee Dey, Dr. Hiral Raja
Country	India
Abstract	In this paper, we develop and refine several fixed-point theorems in the framework of partial metric spaces, a generalization of metric spaces that allow non-zero self-distances. We present improved versions of Banach-type contraction mappings and establish convergence results for various iterative processes, including Mann and Ishikawa iterations, under relaxed contractive conditions. Moreover, we propose a generalized contraction with diminishing error terms and provide corresponding convergence lemmas to support each theorem. Each result is illustrated with suitable examples and is supported by corollaries and auxiliary lemmas. These findings not only unify and extend several known results in the literature but also contribute new tools for analysis in spaces where traditional metric assumptions fail.
Keywords	Partial metric space; Fixed point; Asymptotic complexity; Recursive algorithm; Contractive mapping.
Field	Mathematics
Published In	Volume 7, Issue 3, May-June 2025
Published On	2025-06-14
DOI	https://doi.org/10.36948/ijfmr.2025.v07i03.48099
Short DOI	https://doi.org/g9qqp6

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