Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces

Muhammad SARWAR; Humaira -; Tongxing Lİ

doi:https://doi.org/10.15672/HJMS.2018.633

Article Details

Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces

Authors:

Muhammad SARWAR | Humaira - | Tongxing Lİ

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 6, pp.1712-1728

Document Type:

Article

Publication Date:

12/2019

Document Language:

English

Document ID (Org No.):

2000451346

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/HJMS.2018.633

Abstract:

 


The main purpose of this article is to discuss the existence of the common solution of second-order nonlinear boundary value problems

x′′(ȷ)=k(ȷ,x(ȷ),x′(ȷ)),ifȷ∈[0,Λ],Λ>0,x″(ȷ)=k(ȷ,x(ȷ),x′(ȷ)),ifȷ∈[0,Λ],Λ>0,\mathfrak{x}''(\jmath)=\Bbbk(\jmath,\mathfrak{x}(\jmath),\mathfrak{x}'(\jmath)),\quad\text{if}\:\jmath\in[0,\Lambda],\quad\Lambda>0,

x(ȷ1)=x1,x(ȷ2)=x2,ȷ1,ȷ2∈[0,Λ]x(ȷ1)=x1,x(ȷ2)=x2,ȷ1,ȷ2∈[0,Λ]\mathfrak{x}(\jmath_1)=\mathfrak{x}_1,\quad\mathfrak{x}(\jmath_2)=\mathfrak{x}_2,\quad\jmath_1,\jmath_2\in[0,\Lambda]

where k:[0,Λ]×S(S)×S(S)→S(S)k:[0,Λ]×S(S)×S(S)→S(S)\Bbbk:[0,\Lambda]\times\mathfrak{S}(\mathcal{S})\times\mathfrak{S}(\mathcal{S})\rightarrow\mathfrak{S}(\mathcal{S}) is a continuous function and S(S)S(S)\mathfrak{S}(\mathcal{S}) is a family of fuzzy sets.

  In this regard we obtain common fixed point results for two pairs of fuzzy mappings satisfying rational contractive condition in the setting of complex valued metric spaces. Our results improve those reported in the existing literature.

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Article Details

Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces

Authors: Muhammad SARWAR | Humaira - | Tongxing Lİ

Publisher: Hacettepe University

Main Topics: Mathematics

Journal: Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 6, pp.1712-1728

Document Type: Article

Publication Date: 12/2019

Document Language: English

Document ID (Org No.): 2000451346

Frequency: Bimonthly

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/HJMS.2018.633

Issues

Authors:

Muhammad SARWAR | Humaira - | Tongxing Lİ

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 6, pp.1712-1728

Document Type:

Article

Publication Date:

12/2019

Document Language:

English

Document ID (Org No.):

2000451346

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/HJMS.2018.633