THE PICARD THEOREM ON S-METRIC SPACES

doi:10.1016/S0252-9602(18)30811-7

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1245-1258.doi: 10.1016/S0252-9602(18)30811-7

THE PICARD THEOREM ON S-METRIC SPACES

Nihal Yilmaz ÖZGÜR, Nihal TA?

Department of Mathematics, Bal?kesir University, 10145 Bal?kesir, Turkey

收稿日期:2017-01-25 修回日期:2017-11-20 出版日期:2018-08-25 发布日期:2018-08-25
作者简介:Nihal Yilmaz ÖZGÜR,E-mail:nihal@balikesir.edu.tr;Nihal TAŞ,E-mail:nihaltas@balikesir.edu.tr

THE PICARD THEOREM ON S-METRIC SPACES

Nihal Yilmaz ÖZGÜR, Nihal TA?

Department of Mathematics, Bal?kesir University, 10145 Bal?kesir, Turkey

Received:2017-01-25 Revised:2017-11-20 Online:2018-08-25 Published:2018-08-25

摘要/Abstract

摘要：

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S_∞-space and prove its completeness. We obtain a new generalization of the classical "Picard Theorem".

关键词: S_∞-space, completeness, Picard Theorem, initial value problem

Abstract:

Key words: S_∞-space, completeness, Picard Theorem, initial value problem

Nihal Yilmaz ÖZGÜR, Nihal TAŞ. THE PICARD THEOREM ON S-METRIC SPACES[J]. 数学物理学报(英文版), 2018, 38(4): 1245-1258.

Nihal Yilmaz ÖZGÜR, Nihal TAŞ. THE PICARD THEOREM ON S-METRIC SPACES[J]. Acta mathematica scientia,Series B, 2018, 38(4): 1245-1258.

参考文献 13

[1]	Alsulami H H, Gülyaz S, Karapınar E, Erhan İ M. Fixed point theorems for a class of α-admissible contractions and applications to boundary value problem. Abstr Appl Anal, 2014, Art ID 187031
[2]	Bronson R, Costa G B. Differential Equations. 3rd Ed. Schaum's Outline Series, 2006
[3]	Farajzadeh A P, Kaewcharoen A, Plubtieng S. An application of fixed point theory to a nonlinear differential equation. Abstr Appl Anal, 2014, Art ID 605405
[4]	He F. Some notes on the existence of solution for ordinary differential equations via fixed point theory. Abstr Appl Anal, 2014, Art ID 309613
[5]	Hieu N T, Ly N T, Dung N V. A generalization of ciric quasi-contractions for maps on S-netric spaces. Thai J Math, 2015, 13(2):369-380
[6]	Huang H, Xu S. Fixed point theorems of contractive mappings in cone b-metric spaces and applications. Fixed Point Theory Appl, 2013, 2013:112
[7]	Kakde R V, Biradar S S, Hiremath S S. Solution of differential and integral equations using fixed point theory. Int J Advanced Research Comput Engin Tech, 2014, 3(5):1656-1659
[8]	Krakow J T. Differential equations in metric spaces. Math Bohem, 2002, 127(2):353-360
[9]	Özgür N Y, Taş N. Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25). Math Sci, 2017, 11(1):7-16
[10]	Özgür N Y, Taş N. Some fixed point theorems on S-metric spaces. Mat Vesnik, 2017, 69(1):39-52
[11]	Sedghi S, Shobe N, Aliouche A. A generalization of fixed point theorems in S-metric spaces. Mat Vesnik, 2012, 64(3):258-266
[12]	Sedghi S, Dung N V. Fixed point theorems on S-metric spaces. Mat Vesnik, 2014, 66(1):113-124
[13]	Taş N. Fixed Point Theorems and Their Various Applications[D]. Balikesir:Balikesir Univ, 2017

THE PICARD THEOREM ON S-METRIC SPACES

THE PICARD THEOREM ON S-METRIC SPACES

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献 13

相关文章 7

Metrics

本文评价

推荐阅读 10

[1]	Sun-Ho CHOI, Seung-Yeal HA. ON THE ASYMPTOTIC DYNAMICS OF THE VLASOV-YUKAWA-BOLTZMANN SYSTEM NEAR VACUUM[J]. 数学物理学报(英文版), 2015, 35(4): 887-905.
[2]	李用声, 杨兴雨. GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE[J]. 数学物理学报(英文版), 2011, 31(4): 1303-1317.
[3]	Binod Chandra Tripathy, Bipul Sarma . SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS[J]. 数学物理学报(英文版), 2011, 31(1): 134-140.
[4]	徐桂香, 苑佳. INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS[J]. 数学物理学报(英文版), 2011, 31(1): 15-21.
[5]	姜子文, 庄万. MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 1998, 18(3): 285-292.
[6]	冯学尚. THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION[J]. 数学物理学报(英文版), 1995, 15(2): 196-206.
[7]	王明亮. SYMMETRIES, BÄCKLUND TRANSFORMATIONS AND BOUNDARY-INITIAL VALUE PROBLEMS FOR NONLINEAR CHROMATOGRAPH[J]. 数学物理学报(英文版), 1995, 15(2): 152-160.