Fixed point theorems in b-metric spaces with applications to differential equations

被引：0
作者：
Huaping Huang
Guantie Deng
Stojan Radenović
机构：
[1] Beijing Normal University,Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences
[2] University of Belgrade,Faculty of Mechanical Engineering
来源：
Journal of Fixed Point Theory and Applications | 2018年 / 20卷
关键词：
Picard’s iteration; fixed point; -metric space; -stability; differential equation; 47H10; 54H25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we present some fixed point theorems for a class of contractive mappings in b-metric spaces. We verify the T-stability of Picard’s iteration and the P property for such mappings. We also give an example to support our assertions. In addition, by using our results, we obtain the existence and uniqueness of solution to some ordinary differential equations with initial value conditions. Further, we provide the precise mathematical expressions of solutions to such equations.
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共 38 条
[1]  
Bakhtin IA(1989)The contraction mapping principle in almost metric space (Russian) Funct. Anal. Ulyanovsk. Gos. Ped. Inst. Ulyanovsk 30 26-37
[2]  
Banach S(1922)Sur les operations dans les ensembles abstrait et leur application aux equations, integrals Fundam. Math. 3 133-181
[3]  
Boriceanu M(2010)Multivalued fractals in Cent. Eur. J. Math. 8 367-377
[4]  
Bota M(1993)-metric spaces Acta Math. Inform. Univ. Ostrav. 1 5-11
[5]  
Petruşel A(2017)Contraction mappings in J. Nonlinear Sci. Appl. 10 429-435
[6]  
Czerwik S(2016)-metric spaces J. Comput. Anal. Appl. 20 869-888
[7]  
Huang H(2005)A sharp generalization on cone Fixed Point Theory Appl. 6 71-105
[8]  
Radenović S(2010)-metric space over Banach algebra Fixed Point Theory Appl. 2010 978121-377
[9]  
Deng G(2015)Fixed point theorems and J. Nonlinear Sci. Appl. 8 363-305
[10]  
Huang H(1990)-stability of Picard iteration for generalized Lipschitz mappings in cone metric spaces over Banach algebras J. Math. Anal. Appl. 146 301-2163
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