Fixed Point Theorems in Metric and Banach Spaces with Applications to Economic Equilibrium Analysis
DOI:
https://doi.org/10.69980/ajpr.v28i1.915Keywords:
Fixed Point Theorem, Metric Space, Banach Space, Banach Contraction Principle, Economic Equilibrium, Market Stability, Mathematical Economics, Complete Metric Space, Demand and Supply, Nonlinear Analysis.Abstract
Fixed point theory is one of the most significant branches of nonlinear analysis and has wide applications in mathematics, economics, game theory, optimization, and decision sciences. A fixed point of a mapping is a point that remains unchanged under the action of that mapping. In economic analysis, equilibrium is also a state in which no participant has an incentive to change his or her decision. Thus, the mathematical idea of a fixed point has a natural and powerful connection with economic equilibrium. The present research paper studies fixed point theorems in metric and Banach spaces and explores their applications in economic equilibrium analysis. The study mainly focuses on the Banach contraction principle, its relevance in complete metric spaces, and its usefulness in proving the existence and uniqueness of equilibrium in economic models. The paper further discusses how fixed point methods can be used to analyze price adjustment, demand-supply balance, consumer choice, market stability, and iterative economic decision-making processes. This paper is theoretical and analytical in nature and follows a mathematical research pattern suitable for government university and UGC-oriented academic writing.
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