非阿基米德Menger概率度量空间中Altman型映象公共不动点定理及其在动态规划中的应用
|
摘要
在非阿基米德Menger概率空间中,利用映象对相容条件证明了一类新的Altman型映象的公共不动点定理,从而改进和推广了一些已知结果。作为应用本文还讨论了起源于动态规划的一类泛函方程组解的存在与唯一性。
By using the compatible conditions of self-mapping pair in non-Archimedean Menger probabilistic metric spaces,common fixed point theorems for a class new of Altman type mapping are proved in nonarchimedean Mengerprobabilistic metric spaces,which improve and extend some related corresponding results. As an application we also discuss the existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.
By using the compatible conditions of self-mapping pair in non-Archimedean Menger probabilistic metric spaces,common fixed point theorems for a class new of Altman type mapping are proved in nonarchimedean Mengerprobabilistic metric spaces,which improve and extend some related corresponding results. As an application we also discuss the existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.
引文
[1]ISTRATESCU I,CRIVAT N. On some classes of non-Archimedean probabilistic metric spaces[J]. Seminar de Spatii Metrice Probabiliste,Universitatea Timisoara,Nr,1974,12:13.
[2]ISTRATESCU I. On some fixed point theorems with applications to the nonarchimedean menger spaces.[J]. Atti Accad Naz Lincei,VIII Ser,Rend,Cl Sci Fis Mat Nat,1975,58:374-379.
[3]ISTRATESCU I. Fixed point theorems for some classes of contraction mappings on nonar-chimedean probabilistic metric space[J]. Publ MathDebrecen,1978,25(1/2):29-31.
[4]SEHGAL V M,BHARUCHA-REID T A. Fixed points of contraction mappings on probabilistic metric spaces[J]. Math Systems Theory,1972,6:97.
[5]HADZIC O. A note on Istratescu’s fixed point theorems in non-Archimedean probabilistic metric spaces[J]. Bull. Math Soc Sci Math R S Rou-manie(N S),1980,24(4):359-362.
[6]SINGH S L,PANT B D. Common fixed points of weakly commuting mappings on non-Archimedean Menger PM Spaces[J]. Vikram J Math,1987,6:27-31.
[7]张石生,黄南京,吴定平.非阿基米德Menger概率度量空间中相容映象对的公共不动点定理及应用[J].四川大学学报(自然科学版),1991,28(1)∶19-25.
[8]张石生,向淑文.概率度量空间的拓扑结构和度量化问题及其应用[J].曲阜师范大学学报(自然科学版),1990,16(3):1-9.
[9]CHO Y J,KANG S M,CHANG S S. Coincidence point theorems for nonlinear hybrid contractions in non-Archimedean Menger probabilisticmetric spaces[J].Demonstratio Math,1995,28(1):19-22.
[10]CHO Y J,HA K S,CHANG S S. Common fixed point theorems for compatible mappings of type(A)in Non-Archimedean Menger PM-space[J]. Math Japon,1997,46(1):169-176.
[11]ALMAN M. An integral test for series and generalized contractions[J]. Amer Math Monthly,1975,82(8):827-829.
[12]赵美娜,张树义,郑晓迪. Ciric-Altman型映射的不动点定理[J].西华大学学报(自然科学版),2016,35(6):79-81.
[13]张树义,赵美娜,丛培根.模糊度量空间中Φ-压缩型映象不动点定理及应用[J].南通大学学报(自然科学版),2017,16(3):66-71.
[14]ZHANG S Y,WANG L,SHIN S H,et al. Common fixed point theorems for a pair of orbitally contraction mapping[J]. Fixed Point Theory andApplictions,2003,5:191-195.
[15]郑晓迪,万美玲,张树义.轨道压缩映射的几个新的不动点定理[J].北华大学学报(自然科学版),2014,15(4):438-442.
[16]万美玲,张树义,郑晓迪. 2-距离空间中非唯一不动点定理[J].轻工学报(自然科学版),2017,32(4):105-108.
[17]刘冬红,张树义,郑晓迪. 2-距离空间中一类压缩型映象的不动点定理[J].南通大学学报(自然科学版),2016,15(2):68-74.
[18]张树义,宋晓光,栾丹.Φ-压缩映象的公共不动点定理[J].北华大学学报(自然科学版),2014,15(2):162-166.
[19]赵美娜,张树义.关于2-渐近正则映象的一个注记[J].鲁东大学学报(自然科学版),2016,32(3):193-197.
[20]林媛,丛培根,张树义.广义C-映象不动点的存在性[J].南通大学学报(自然科学版),2017,16(2):66-69.
[21]赵美娜,张树义,郑晓迪. 2-距离空间中Fisher型映象的公共不动点定理[J].杭州师范大学学报(自然科学版),2016,15(6):632-635.
[22]张树义,丛培根,林媛.有限族严格伪压缩映像公共不动点的强收敛定理[J].西华大学学报(自然科学版),2018,37(1):39-45.
[2]ISTRATESCU I. On some fixed point theorems with applications to the nonarchimedean menger spaces.[J]. Atti Accad Naz Lincei,VIII Ser,Rend,Cl Sci Fis Mat Nat,1975,58:374-379.
[3]ISTRATESCU I. Fixed point theorems for some classes of contraction mappings on nonar-chimedean probabilistic metric space[J]. Publ MathDebrecen,1978,25(1/2):29-31.
[4]SEHGAL V M,BHARUCHA-REID T A. Fixed points of contraction mappings on probabilistic metric spaces[J]. Math Systems Theory,1972,6:97.
[5]HADZIC O. A note on Istratescu’s fixed point theorems in non-Archimedean probabilistic metric spaces[J]. Bull. Math Soc Sci Math R S Rou-manie(N S),1980,24(4):359-362.
[6]SINGH S L,PANT B D. Common fixed points of weakly commuting mappings on non-Archimedean Menger PM Spaces[J]. Vikram J Math,1987,6:27-31.
[7]张石生,黄南京,吴定平.非阿基米德Menger概率度量空间中相容映象对的公共不动点定理及应用[J].四川大学学报(自然科学版),1991,28(1)∶19-25.
[8]张石生,向淑文.概率度量空间的拓扑结构和度量化问题及其应用[J].曲阜师范大学学报(自然科学版),1990,16(3):1-9.
[9]CHO Y J,KANG S M,CHANG S S. Coincidence point theorems for nonlinear hybrid contractions in non-Archimedean Menger probabilisticmetric spaces[J].Demonstratio Math,1995,28(1):19-22.
[10]CHO Y J,HA K S,CHANG S S. Common fixed point theorems for compatible mappings of type(A)in Non-Archimedean Menger PM-space[J]. Math Japon,1997,46(1):169-176.
[11]ALMAN M. An integral test for series and generalized contractions[J]. Amer Math Monthly,1975,82(8):827-829.
[12]赵美娜,张树义,郑晓迪. Ciric-Altman型映射的不动点定理[J].西华大学学报(自然科学版),2016,35(6):79-81.
[13]张树义,赵美娜,丛培根.模糊度量空间中Φ-压缩型映象不动点定理及应用[J].南通大学学报(自然科学版),2017,16(3):66-71.
[14]ZHANG S Y,WANG L,SHIN S H,et al. Common fixed point theorems for a pair of orbitally contraction mapping[J]. Fixed Point Theory andApplictions,2003,5:191-195.
[15]郑晓迪,万美玲,张树义.轨道压缩映射的几个新的不动点定理[J].北华大学学报(自然科学版),2014,15(4):438-442.
[16]万美玲,张树义,郑晓迪. 2-距离空间中非唯一不动点定理[J].轻工学报(自然科学版),2017,32(4):105-108.
[17]刘冬红,张树义,郑晓迪. 2-距离空间中一类压缩型映象的不动点定理[J].南通大学学报(自然科学版),2016,15(2):68-74.
[18]张树义,宋晓光,栾丹.Φ-压缩映象的公共不动点定理[J].北华大学学报(自然科学版),2014,15(2):162-166.
[19]赵美娜,张树义.关于2-渐近正则映象的一个注记[J].鲁东大学学报(自然科学版),2016,32(3):193-197.
[20]林媛,丛培根,张树义.广义C-映象不动点的存在性[J].南通大学学报(自然科学版),2017,16(2):66-69.
[21]赵美娜,张树义,郑晓迪. 2-距离空间中Fisher型映象的公共不动点定理[J].杭州师范大学学报(自然科学版),2016,15(6):632-635.
[22]张树义,丛培根,林媛.有限族严格伪压缩映像公共不动点的强收敛定理[J].西华大学学报(自然科学版),2018,37(1):39-45.