The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theoremwas generalized byAoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has pr...

In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let A1, . . . , Am ⊆ R be subsets with finite Lebesgue measure. Then, for any sequence f0, . . . , fm of R-linearly independent polynomials in the polynomial ring R[X1, . . . , Xn] there are real numbers λ0, . . . , λm, not all zero, such that ...

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, prove an existence result. We also investigate the uniqueness solution using Banach contraction principle. Moreover, study Ulam-Hyers stability and generalized-Ulam-Hyers solutions. Some illustrative examples are presented.

An S] version of the Borsuk-Ulam Theorem is proved for a situation where Fix S1 may be nontrivial. The proof is accomplished with the aid of a new relative index theory. Applications are given to intersection theorems and the existence of multiple critical points is established for a class of functional invariant under an S' symmetry. Introduction. One of the variants of the Borsuk-Ulam Theorem...

Abstract We establish inter alia a compactness criterion in metric spaces involving sequence of completely continuous mappings, which is continuously convergent, the sense H. Hahn, to identity mapping. For Banach spaces, linear version that result coincides with theorem due Mazur. also present new proof Ascoli–Arzelà theorem, we use above applied Bernstein operators.

We generalize a theorem of Mazur concerning the universal norms of an abelian variety over a Zp-extension of a complete local field. Then we apply it to the proof of a control theorem for abelian varieties over global function fields.

The main result of this note is a parametrized version of the BorsukUlam theorem. Loosely speaking, it states that for a map X × S → S (with k < n), considered as a family of maps from S to S, the set of solutions to the Borsuk-Ulam problem (i.e. opposite points in S with the same value) depends continuously on X. We actually formuate this for correspondences. The “continuity” is measured by th...