Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric prope...We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.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
Background: Among elderly people, rehabilitation is important for reducing the risk of falls and hospitalization and to maintain an independent life for longer. Motivation is a factor for elderly people to lead an act...Background: Among elderly people, rehabilitation is important for reducing the risk of falls and hospitalization and to maintain an independent life for longer. Motivation is a factor for elderly people to lead an active daily life and leave home more frequently. Purpose: The purposes of this study were to determine the optimal cut-off point in the Scale for Achievement Motive in Geriatrics (SAMG) that could identify individuals as inactive or active, based on the Frenchay Activities Index (FAI), and to compare characteristics between active and inactive groups classified by the cut-off point. Methods: A cross-sectional study of 285 community-dwelling elderly people measured SAMG and FAI and physical function. Receiver operating characteristic (ROC) analysis was used to calculate the area under the curve (AUC) that was the optimal cut-off point for the SAMG total score, with the associated sensitivity and 1-specificity when compared with the FAI results. Demographic parameters and physical function were compared between two groups defined by cut-off point. Results: The AUC was 0.78, the optimal cut-off for SAMG total score for indicating inactivity was ≤48, the sensitivity was 77.98% and the 1-specificity was 75.00%. The group with SAMG score >48 was characterized by a significantly higher proportion of women, fewer people sharing a house, and participation in more hobbies. Discussion: A cut-off point of 48 in the SAMG could be a predictive index of motivation toward goals for individuals with inactive daily activities. The group with score higher than the cut-off was characterized by more women, fewer people living together, and more hobbies than the group with lower scores.展开更多
Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
Approaches to the artificial impoundment and theoretical design of sedimentation retention basin are reviewed with particular attention to best management practice(BMP) to control agriculture and surface runoff. Sedim...Approaches to the artificial impoundment and theoretical design of sedimentation retention basin are reviewed with particular attention to best management practice(BMP) to control agriculture and surface runoff. Sediments retention basins are the small version of farm pond used where a criteria of farm pond is not met. Such basin traps the pollutants and suspended solids prior to entry into streams and lakes. The study is focused with special reference to the assessment and control of non point source pollution(NPSP) from the sub basin area of Tai Lake in the Xishan County of Wuxi City of China. The author suggested two different approaches to conduct this study including theoretical design for sedimentation retention basin and computation of flow, sediment transport and deposition during the artificial impoundment of retention basin for BMP's utilization. Theoretical design will provide a useful function as a first line defense against the movement of sediments and transport of pollutants into the Tai Lake while the assessment of sediments deposition will help to make its proper use and periodic cleanup.展开更多
In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type f...In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.展开更多
In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obta...In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.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
We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map stud...We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.展开更多
文摘Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
文摘We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.
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Background: Among elderly people, rehabilitation is important for reducing the risk of falls and hospitalization and to maintain an independent life for longer. Motivation is a factor for elderly people to lead an active daily life and leave home more frequently. Purpose: The purposes of this study were to determine the optimal cut-off point in the Scale for Achievement Motive in Geriatrics (SAMG) that could identify individuals as inactive or active, based on the Frenchay Activities Index (FAI), and to compare characteristics between active and inactive groups classified by the cut-off point. Methods: A cross-sectional study of 285 community-dwelling elderly people measured SAMG and FAI and physical function. Receiver operating characteristic (ROC) analysis was used to calculate the area under the curve (AUC) that was the optimal cut-off point for the SAMG total score, with the associated sensitivity and 1-specificity when compared with the FAI results. Demographic parameters and physical function were compared between two groups defined by cut-off point. Results: The AUC was 0.78, the optimal cut-off for SAMG total score for indicating inactivity was ≤48, the sensitivity was 77.98% and the 1-specificity was 75.00%. The group with SAMG score >48 was characterized by a significantly higher proportion of women, fewer people sharing a house, and participation in more hobbies. Discussion: A cut-off point of 48 in the SAMG could be a predictive index of motivation toward goals for individuals with inactive daily activities. The group with score higher than the cut-off was characterized by more women, fewer people living together, and more hobbies than the group with lower scores.
文摘Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
文摘Approaches to the artificial impoundment and theoretical design of sedimentation retention basin are reviewed with particular attention to best management practice(BMP) to control agriculture and surface runoff. Sediments retention basins are the small version of farm pond used where a criteria of farm pond is not met. Such basin traps the pollutants and suspended solids prior to entry into streams and lakes. The study is focused with special reference to the assessment and control of non point source pollution(NPSP) from the sub basin area of Tai Lake in the Xishan County of Wuxi City of China. The author suggested two different approaches to conduct this study including theoretical design for sedimentation retention basin and computation of flow, sediment transport and deposition during the artificial impoundment of retention basin for BMP's utilization. Theoretical design will provide a useful function as a first line defense against the movement of sediments and transport of pollutants into the Tai Lake while the assessment of sediments deposition will help to make its proper use and periodic cleanup.
基金This work is supported by the Scientific Research Foundation of Bijie University.
文摘In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.
文摘In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.
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 .
文摘We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.
基金Supported by the National Natural Science Foundation of China(12161056,11701259,11771198)Natural Science Foundation of Jiangxi Province of China(20202BAB201001)。
