In this paper we consider several generalizations of the Borsuk–Ulam theorem for G-spaces and apply these results to Tucker type lemmas G-simplicial complexes PL-manifolds.

In 1940, Ulam [13] proposed the Ulam stability problem of additive mappings. In the next year, Hyers [5] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L is the unique additive mapping s...

We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense. © 2007 Elsevier B.V. All rights reserved. MSC: primary 46S40secondary 39B52 39B82 26E50 46S50

The Borsuk-Ulam theorem states that a continuous function f : S → R has a point x ∈ S with f(x) = f(−x). We give an analogue of this theorem for digital images, which are modeled as discrete spaces of adjacent pixels equipped with Z-valued functions. In particular, for a concrete two-dimensional rectangular digital image whose pixels all have an assigned “brightness” function, we prove that the...

This article deals with the optimal control of fractional stochastic nonlocal semilinear system in Hilbert space. The existence and uniqueness results for mild solution are derived using Banach fixed point theorem. is proved minimizing sequence approach Mazur?s lemma. For better understanding theory, we have included one example.

In 1940 and in 1968 S. M. Ulam proposed the general problem:”When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941 D. H. Hyers solved this stability problem for linear mappings. In 1951 D. G. Bourgin was the second author to treat the same problem for additive mappings. According to...