We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

The Nakai–Nishimura–Dubois–Efroymson dimension theorem asserts the following: “Let R be an algebraically closed field or a real closed field, let X be an irreducible algebraic subset of Rn and let Y be an algebraic subset of X of codimension s ≥ 2 (not necessarily irreducible). Then, there is an irreducible algebraic subset W of X of codimension 1 containing Y ”. In this paper, making use of an...

In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

We adopt the following convention: x, y are real numbers, i, j, k are natural numbers, and p, q are finite sequences of elements of R. The following propositions are true: (1) Let A be a closed-interval subset of R and D be an element of divsA. If vol(A) 6= 0, then there exists i such that i ∈ domD and vol(divset(D, i)) > 0. (2) Let A be a closed-interval subset of R, D be an element of divsA, ...