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
  • [11] Xu S(2017)Maps for which J. Fixed Point Theory Appl. 19 2153-29
  • [12] Liu H(1995)Common fixed point results in metric-type spaces J. Niger. Math. Soc. 14–15 17-13
  • [13] Radenović S(2008)Various Suzuki type theorems in Fixed Point Theory Appl. 2008 418971-600
  • [14] Jeong GS(2018)-metric spaces Vietnam J. Math. 46 5-416
  • [15] Rhoades BE(2016)A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 110 585-145
  • [16] Jovanović M(2016)New fixed point theorems for set-valued contractions in J. Fixed Point Theory Appl. 18 397-undefined
  • [17] Kadelburg Z(2015)-metric spaces Fixed Point Theory Appl. 2015 164-undefined
  • [18] Radenović S(2016)Stability results for fixed point iteration procedures Open Math. 14 128-undefined
  • [19] Latif A(undefined)-Stability of Picard iteration in metric spaces undefined undefined undefined-undefined
  • [20] Parvaneh V(undefined)Generic well-posedness of fixed point problems undefined undefined undefined-undefined
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