In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply ou...In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.展开更多
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
Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and as...Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.展开更多
基金Tsupported by the National Natural Science Foundation of China(No.11971234,11671193)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain T;.We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.
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].
基金Foundation item： the National Natural Science Foundation of China （No. 10771141） the Natural Science Foundation of Zhejiang Province （Y605191） the Natural Science Foundation of Heilongjiang Province （No. A0211） and the Scientific Research Foundation from Zhejiang Province Education Committee （No. 20051897）.
文摘Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.
