CAJ | 학술논문

设K是实Banach空间E中非空闭凸集,{Ti}i=1N是N个具公共不动点集F的严格伪压缩映像,{an}(∩)[0,1]是实数列,{un})(∩)K是序列,且满足下面条件(ii)∑n=1(1-an)=+∞;(iii)∑n∞=1‖un‖＜+∞.设x0∈K,{xn}由下式定义 xn=anxn-1+(1-an)Tnxn+un-1,n≥1,其中Tn=TnmodN,则有下面结论(i)limn→∞‖xn-p‖存在,对所有p∈F;(ii)limn→∞d(xn,F)存在,当d(xn,F)=infp∈F‖xn-p‖;(iii)lim in fn→∞‖xn-Tnxn‖=0.文中另一个结果是,如果{xn}(∩)[1-2-n,1],则{xn}收敛.文中结果改进与扩展了Osilike(2004) 最近的结果,证明方法也不同.
설K시실Banach공간E중비공폐철집,{Ti}i=1N시N개구공공불동점집F적엄격위압축영상,{an}(∩)[0,1]시실수렬,{un})(∩)K시서렬,차만족하면조건(ii)∑n=1(1-an)=+∞;(iii)∑n∞=1‖un‖＜+∞.설x0∈K,{xn}유하식정의 xn=anxn-1+(1-an)Tnxn+un-1,n≥1,기중Tn=TnmodN,칙유하면결론(i)limn→∞‖xn-p‖존재,대소유p∈F;(ii)limn→∞d(xn,F)존재,당d(xn,F)=infp∈F‖xn-p‖;(iii)lim in fn→∞‖xn-Tnxn‖=0.문중령일개결과시,여과{xn}(∩)[1-2-n,1],칙{xn}수렴.문중결과개진여확전료Osilike(2004) 최근적결과,증명방법야불동.
Let E be a real Banach space and K be a nonempty closed convex subset of E.Let {Ti}iN=1 be N strictly pseudocontractive self-maps of K such that F=∩Ni=1 F(Ti)≠φ,where F(Ti)={x∈K:Tix=x},{an}(∩)[0,1] be a real sequence,and {un}(∩)K be a sequence satisfying the conditions:(i)0＜a≤an≤1;(ii)∑n∞=1(1-an)=+∞;(iii)∑n∞=1⊥‖un‖＜+∞.Let xo ∈K and {xn}n∞=1 be defined by xn=anxn-1+(1-an)Tnxn+un-1,n≥1,where Tn=TnmodN,then (i)limn→∞‖xn-p‖ exists for all P∈F;(ii)limn→∞ d(xn,F) exists,where d(xn,F)=infp∈F‖xn-p‖;(iii)lim infn→∞‖xn-Tnxn‖=0.Another result is that if{an}∞n=1(∩)[1-2-n,1],then {xn} is convergent. This paper generalizes and improves the results of Osilike in 2004.The ideas and.proof fines used in this paper are different from those of Osilike in 2004.