On the Mean Iteration ( a , b ) + ( a + 3 b x ? + b
نویسنده
چکیده
The iterative process an+1 = (an + 3bn)/4, bn+1 = ( +bn )/2 is studied in detail. The limit of this quadratically converging process is explicitly identified, as are the uniformizing parameters. The role of symbolic computation, in discovering these nontrivial identifications, is highlighted.
منابع مشابه
Some weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
متن کاملLie higher derivations on $B(X)$
Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.
متن کاملB -AND B - COMPLETENESS IN LOCALLY CONVEX ALGEBRAS AND THE E x THEOREM
Let E be a B-complete (B -complete) locally convex algebra and $ the topological direct sum of countably many copies of the scalar field with a jointly continuous algebra multiplication. It has been shown that E is also B-complete (B -complete) for componentwise multiplication on E . B-and Br-completeness of E , the unitization of E, and also of E x for other multiplications on E ...
متن کاملThe Asymptotic Form of Eigenvalues for a Class of Sturm-Liouville Problem with One Simple Turning Point
The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کاملA Certain Class of Character Module Homomorphisms on Normed Algebras
For two normed algebras $A$ and $B$ with the character space $bigtriangleup(B)neq emptyset$ and a left $B-$module $X,$ a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$ as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...
متن کامل