For a subset K of a metric space (X,d) and x ∈ X,Px(x)={y ∈ K : d(x,y) = d(x,K)≡ inf{d(x,k) : k ∈ K}}is called the set of best K-approximant to x. An element go E K is said to be a best simulta- neous ...For a subset K of a metric space (X,d) and x ∈ X,Px(x)={y ∈ K : d(x,y) = d(x,K)≡ inf{d(x,k) : k ∈ K}}is called the set of best K-approximant to x. An element go E K is said to be a best simulta- neous approximation of the pair y1,y2 E ∈ if max{d(y1,go),d(y2,go)}=inf g∈K max {d(y1,g),d(y2,g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T- and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas^[1], S. Chandok and T.D. Narang^[2], T.D. Narang and S. Chandok^[11], S.A. Sahab, M.S. Khan and S. Sessa^[14], P. Vijayaraju^[20] and P. Vijayaraju and M. Marudai^[21].展开更多
We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into ...We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .展开更多
文摘For a subset K of a metric space (X,d) and x ∈ X,Px(x)={y ∈ K : d(x,y) = d(x,K)≡ inf{d(x,k) : k ∈ K}}is called the set of best K-approximant to x. An element go E K is said to be a best simulta- neous approximation of the pair y1,y2 E ∈ if max{d(y1,go),d(y2,go)}=inf g∈K max {d(y1,g),d(y2,g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T- and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas^[1], S. Chandok and T.D. Narang^[2], T.D. Narang and S. Chandok^[11], S.A. Sahab, M.S. Khan and S. Sessa^[14], P. Vijayaraju^[20] and P. Vijayaraju and M. Marudai^[21].
文摘We propose a class of iteration methods searching the best approximately generalized polynomial, which has parallel computational function and converges to the exact solution quadratically. We first transform it into a special system of nonlinear equations with constraint, then by using to certain iteration method, we combine the two basic processes of the Remes method into a whole such that the iterative process of the system of nonlinear equations and the computation of the solution to the system of linear equations proceed alternately. A lot of numerical examples show that this method not only has good convergence property but also always converges to the exact solution of the problem accurately and rapidly for almost all initial approximations .