• Dr. Raja Ram Singh
• Sourabh Kumar
• Laxman Kumar Rai
• Sanjay Kumar
• Ravish Kumar Nirdosh

In this paper, we establish several unique fixed point (UFP) results in a Real Metric (RM) space using a novel set-based iteration framework. Set-based iteration function provide a natural and robust extension of classical iteration by allowing mapping from element to subsets of the underlying space. The approach is based on the construction of an ordered pair G-set and its associated G₀-subset, generated through iterative sequences of a self-mapping. Unlike classical pointwise iterations, the proposed framework interprets the iteration process as a sequence of subsets governed by metric distances. We prove the existence and uniqueness of fixed-points for Banach, Kannan, Chatterjea, and generalized contractive mappings by analyzing the monotonic behaviour of an associated distance T- sequence. The completeness of the metric space ensures convergence, while the contraction conditions guarantee uniqueness. The results unify and extend several classical fixed point theorems and provide a flexible structure applicable to nonlinear analysis, optimization, coding theory, and control systems. The exposition is self-contained and written to meet contemporary research standards.

Set-based iteration, unique fixed point, G-set, G₀-subset, metric space, contraction mapping, monotone sequence

"Fixed Point Results in Metric Spaces Using Set-based Iteration Functions", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.13, Issue 3, page no.b295-b303, March-2026, Available :http://www.jetir.org/papers/JETIR2603137.pdf

"Fixed Point Results in Metric Spaces Using Set-based Iteration Functions", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.13, Issue 3, page no. ppb295-b303, March-2026, Available at : http://www.jetir.org/papers/JETIR2603137.pdf