弱压缩多值映射的公共不动点定理
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摘要
在完备的度量空间中,利用泛函分析和集值映射的理论工具,研究了已有文献提出的一个问题并给出了正面回答,即建立了满足φ-弱压缩性质的2个多值映射的公共不动点定理,把公共不动点定理推广到了2个多值映射.
In the complete metric space,a problem posed by the literature and a positive answer is given using the theoretical tods of functional analysis and set-valued mapping. The common fixed point theorem of two multivalued generalized φ-weak contractive mappings is established. This theorem is a generalization of the common fixed point theorem for two multi-valued maps.
In the complete metric space,a problem posed by the literature and a positive answer is given using the theoretical tods of functional analysis and set-valued mapping. The common fixed point theorem of two multivalued generalized φ-weak contractive mappings is established. This theorem is a generalization of the common fixed point theorem for two multi-valued maps.
引文
[1]Rouhani B D,Moradi S.Common fixed point of multivalued generalized-weak contractive mapping[J].Fixed Point Theory and Applications,2010,2010(1):1-13.
[2]Daffer P Z,Kaneko H.Fixed points of generalized contractive multi-valued mappings[J].Journal of Mathematical Analysis and Applications,1995,192(2):655-666.
[3]Abbas M,Rhoades B E,Nazir T.Common fixed points of generalized contractive multivalued mappings in cone metric spaces[J].Mathematical Commmunication,2009,14(2):365-378.
[4]Cho S H,Kim M S.Fixed point theorems for general contractive multivalued mappings[J].J Appl Math Informatics,2009,27(1/2):343-350.
[5]Kiran Q,Kamran T.Fixed point theorems for generalized contractive multi-valued maps[J].Computers and Mathematics with Applications,2010,59(12):3813-3823.
[6]Abkar A,Eslamian M.Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces[J].Fixed Point Theory and Applications,2010,2010(2):1-10.
[7]Zhang Xian.Fixed point theorems of multivalued monotone mapping in ordered metric spaces[J].Computers and Mathematics with Applications,2010,23(3):235-240.
[8]Chifu C,Petrusel G.Existence and data dependence of fixed points and strict fixed points for contractive-type multivalued operators[J].Fixed Point Theory and Applications,2007,2007(1):1-8.
[9]Assad N A,Kirk W A.Fixed point theorems for set-valued mappings of contractive type[J].Pacific Journal of Mathematics,1972,43(3):553-562.
[10]甘会林.整函数差分的零点和不动点[J].江西师范大学学报:自然科学版,2015,39(5):519-521.
[11]金瑾.单位圆内高阶齐次线性微分方程解与不动点的研究[J].江西师范大学学报:自然科学版,2013,37(4):406-410.
[12]李效敏,仪洪勋,张学.涉及复合亚纯函数和不动点的亚纯函数的正规族[J].江西师范大学学报:自然科学版,2016,40(6):578-586.
[13]王金明,郑雄军.半序空间混合单调算子的耦合不动点定理及其应用[J].江西师范大学学报:自然科学版,2014,38(3):240-243.
[14]Zhao Jingyun,Ding Huisheng,N'Guérékata G M.Positive almost periodic solutions to integral equations with superlinear perturbations via a new fixed point theorem in cones[J].Electron J Differential Equations,2017,2017(2):1-10.
[15]Ding Huisheng,Ozturk Vi,Radenovic'S.On some new fixed point results in b-rectangular metric spaces[J].J Nonlinear Sci Appl,2015,8(4):378-386.
[2]Daffer P Z,Kaneko H.Fixed points of generalized contractive multi-valued mappings[J].Journal of Mathematical Analysis and Applications,1995,192(2):655-666.
[3]Abbas M,Rhoades B E,Nazir T.Common fixed points of generalized contractive multivalued mappings in cone metric spaces[J].Mathematical Commmunication,2009,14(2):365-378.
[4]Cho S H,Kim M S.Fixed point theorems for general contractive multivalued mappings[J].J Appl Math Informatics,2009,27(1/2):343-350.
[5]Kiran Q,Kamran T.Fixed point theorems for generalized contractive multi-valued maps[J].Computers and Mathematics with Applications,2010,59(12):3813-3823.
[6]Abkar A,Eslamian M.Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces[J].Fixed Point Theory and Applications,2010,2010(2):1-10.
[7]Zhang Xian.Fixed point theorems of multivalued monotone mapping in ordered metric spaces[J].Computers and Mathematics with Applications,2010,23(3):235-240.
[8]Chifu C,Petrusel G.Existence and data dependence of fixed points and strict fixed points for contractive-type multivalued operators[J].Fixed Point Theory and Applications,2007,2007(1):1-8.
[9]Assad N A,Kirk W A.Fixed point theorems for set-valued mappings of contractive type[J].Pacific Journal of Mathematics,1972,43(3):553-562.
[10]甘会林.整函数差分的零点和不动点[J].江西师范大学学报:自然科学版,2015,39(5):519-521.
[11]金瑾.单位圆内高阶齐次线性微分方程解与不动点的研究[J].江西师范大学学报:自然科学版,2013,37(4):406-410.
[12]李效敏,仪洪勋,张学.涉及复合亚纯函数和不动点的亚纯函数的正规族[J].江西师范大学学报:自然科学版,2016,40(6):578-586.
[13]王金明,郑雄军.半序空间混合单调算子的耦合不动点定理及其应用[J].江西师范大学学报:自然科学版,2014,38(3):240-243.
[14]Zhao Jingyun,Ding Huisheng,N'Guérékata G M.Positive almost periodic solutions to integral equations with superlinear perturbations via a new fixed point theorem in cones[J].Electron J Differential Equations,2017,2017(2):1-10.
[15]Ding Huisheng,Ozturk Vi,Radenovic'S.On some new fixed point results in b-rectangular metric spaces[J].J Nonlinear Sci Appl,2015,8(4):378-386.