Flesh firmness(FF) is an important and complex trait for melon breeders and consumers. However, the genetic mechanism underlying FF is unclear. Here, a soft fruit melon(P5) and a hard fruit melon(P10) were crossed to ...Flesh firmness(FF) is an important and complex trait for melon breeders and consumers. However, the genetic mechanism underlying FF is unclear. Here, a soft fruit melon(P5) and a hard fruit melon(P10) were crossed to generate F2, and the FF and fruit-related traits were recorded for two years. By performing quantitative trait locus(QTL) specificlocus amplified fragment(SLAF)(QTL-SLAF) sequencing and molecular marker-linkage analysis, 112 844 SLAF markers were identified, and 5 919 SNPs were used to construct a genetic linkage map with a total genetic distance of1 356.49 cM. Ten FF-and fruit-related QTLs were identified. Consistent QTLs were detected for fruit length(FL) and fruit diameter(FD) in both years, and QTLs for single fruit weight(SFW) were detected on two separate chromosomes in both years. For FF, the consistent major locus(ff2.1) was located in a 0.17-Mb candidate region on chromosome 2. Using 429 F2individuals derived from a cross between P5 and P10, we refined the ff2.1 locus to a 28.3-kb region harboring three functional genes. These results provide not only a new candidate QTL for melon FF breeding but also a theoretical foundation for research on the mechanism underlying melon gene function.展开更多
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c...The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).展开更多
In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive...In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.展开更多
For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY...For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.展开更多
A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty ...A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).展开更多
A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions ar...A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.展开更多
Some generalizations of the result proved by S.P. Singh [J. Approx. Theory 25（1979）, 89-90] are presented in convex metric spaces. The results proved contain several known results on the subject.
基金supported by the grants from the National Natural Science Foundation of China (31772330 and 32002043)the Natural Science Foundation of the Heilongjiang Province, China (LH2022C065)the Heilongjiang Bayi Agricultural University Support Program for SanHengSanZong, China (TDJH202004)。
文摘Flesh firmness(FF) is an important and complex trait for melon breeders and consumers. However, the genetic mechanism underlying FF is unclear. Here, a soft fruit melon(P5) and a hard fruit melon(P10) were crossed to generate F2, and the FF and fruit-related traits were recorded for two years. By performing quantitative trait locus(QTL) specificlocus amplified fragment(SLAF)(QTL-SLAF) sequencing and molecular marker-linkage analysis, 112 844 SLAF markers were identified, and 5 919 SNPs were used to construct a genetic linkage map with a total genetic distance of1 356.49 cM. Ten FF-and fruit-related QTLs were identified. Consistent QTLs were detected for fruit length(FL) and fruit diameter(FD) in both years, and QTLs for single fruit weight(SFW) were detected on two separate chromosomes in both years. For FF, the consistent major locus(ff2.1) was located in a 0.17-Mb candidate region on chromosome 2. Using 429 F2individuals derived from a cross between P5 and P10, we refined the ff2.1 locus to a 28.3-kb region harboring three functional genes. These results provide not only a new candidate QTL for melon FF breeding but also a theoretical foundation for research on the mechanism underlying melon gene function.
文摘The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).
文摘In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
基金the National Natural Science Foundation of China(No.10461006)the Natural Science Foundation of Shandong Province(Y002A10)the Younger Foundation of Yantai University(SX05Z9)
文摘For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.
基金supported by Korea Research Foundation Grant(KRF-2001-005-D00002)
文摘A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).
基金supported by the Natural Science Foundation of Yibin University (No.2009Z3)
文摘A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.
基金This research is partially supported by University Grants Commission, India (F30-238/2004(SR)).
文摘Some generalizations of the result proved by S.P. Singh [J. Approx. Theory 25（1979）, 89-90] are presented in convex metric spaces. The results proved contain several known results on the subject.
