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2 years ago in Mathematical Analysis By Sourabh

How can one study fixed point theory in different spaces, including random fixed points?

My work in economic equilibrium modeling has led me to fixed point theorems. I need to build a rigorous understanding from classical results in metric spaces to their modern applications in stochastic analysis and random operator theory. A guided roadmap from fundamentals to research frontier would be invaluable.

 

DerivativePoints RandomOperators

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By Krirthi Answered 1 year ago

I would recommend a tiered approach. First, master the classics in complete metric spaces: the Banach Contraction Principle and Brouwer's theorem. Use a text like "Granas & Dugundji" for depth. Then, move to more abstract topological fixed point theory (e.g., Schauder, Tychonoff theorems). For the random case, which I've applied in stochastic modeling, you need a firm grasp of measurable selections and probability in function spaces. Start with papers by Itoh, Spacek, or Bharucha-Reid to see how classical conditions are adapted to a probabilistic milieu.

 

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