arXiv subjects

Ranjit Vohra

Publications and source records attributed to Ranjit Vohra.

3 recordsLinked to original sources

arXiv2026

A Further Generalization of the Gale-Nikaido-Kuhn-Debreu Market Equilibrium Theorem

We extend the important generalizations by Yannelis [25] and Cornet et al [7] of the classical result of Gale, Nikaido, Kuhn and Debreu (the "GNKD theorem") regarding existence of market equilibrium, by broadening the applicability of their results, which apply only to economies with commodity space that can be modeled by a locally convex Hausdorff space, to the wider class of economies with commodity spaces describable by any Hausdorff topological vector space with nontrivial continuous dual.

math.FA↗

arXiv2025

A Generalization of the "Brouwer-Schauder-Tychonoff" Fixed-Point Theorem

We prove a new fixed - point result for the image Im(j) of any continuous function j from K to (K x K), where K is a compact convex subset of a Hausdorff locally convex space, provided that the projection of Im(j) to the first factor is onto, and a condition on the convex hull of Im(j) holds. A special case of our result is the Brouwer - Schauder - Tychonoff fixed point theorem for continuous functions from K to K.

math.FA↗

arXiv2025

A General Fixed-Point Theorem for Correspondences

A new local condition on correspondences called the "weak local connectedness property" (WLCP) is introduced. Working in ZFC, it is shown in our main theorem that - under mild restrictions - any correspondence from a connected subset X of a real TVS to itself will have a fixed point if the WLCP holds at each point of the domain. Since the WLCP generalizes several well - known conditions on correspondences, it is utilized in this paper to gather together a sampling of several disparate fixed-point and related results that are special cases of our main theorem.

math.GM↗