Year 2019, Volume 48 , Issue 6, Pages 1712 - 1728 2019-12-08

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

Muhammad SARWAR [1] , Humaira - [2] , Tongxing Lİ [3]


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

$$\mathfrak{x}''(\jmath)=\Bbbk(\jmath,\mathfrak{x}(\jmath),\mathfrak{x}'(\jmath)),\quad\text{if}\:\jmath\in[0,\Lambda],\quad\Lambda>0,$$

$$\mathfrak{x}(\jmath_1)=\mathfrak{x}_1,\quad\mathfrak{x}(\jmath_2)=\mathfrak{x}_2,\quad\jmath_1,\jmath_2\in[0,\Lambda]$$

where $\Bbbk:[0,\Lambda]\times\mathfrak{S}(\mathcal{S})\times\mathfrak{S}(\mathcal{S})\rightarrow\mathfrak{S}(\mathcal{S})$ is a continuous function and $\mathfrak{S}(\mathcal{S})$ 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.

Complex valued metric space, Fuzzy mapping, Fixed point, Common fixed point, Cauchy sequence, Contractive condition
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-3904-8442
Author: Muhammad SARWAR (Primary Author)
Institution: University of Malakand
Country: Pakistan


Orcid: 0000-0002-8456-6997
Author: Humaira -
Institution: University of Malakand
Country: Pakistan


Orcid: 0000-0002-4039-9648
Author: Tongxing Lİ
Institution: Linyi University
Country: China


Dates

Publication Date : December 8, 2019

Bibtex @research article { hujms479179, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1712 - 1728}, doi = {10.15672/HJMS.2018.633}, title = {Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces}, key = {cite}, author = {SARWAR, Muhammad and -, Humaira and Lİ, Tongxing} }
APA SARWAR, M , -, H , Lİ, T . (2019). Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1712-1728 . DOI: 10.15672/HJMS.2018.633
MLA SARWAR, M , -, H , Lİ, T . "Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1712-1728 <https://dergipark.org.tr/en/pub/hujms/issue/50516/479179>
Chicago SARWAR, M , -, H , Lİ, T . "Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1712-1728
RIS TY - JOUR T1 - Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces AU - Muhammad SARWAR , Humaira - , Tongxing Lİ Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.633 DO - 10.15672/HJMS.2018.633 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1712 EP - 1728 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.633 UR - https://doi.org/10.15672/HJMS.2018.633 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces %A Muhammad SARWAR , Humaira - , Tongxing Lİ %T Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.633 %U 10.15672/HJMS.2018.633
ISNAD SARWAR, Muhammad , -, Humaira , Lİ, Tongxing . "Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1712-1728 . https://doi.org/10.15672/HJMS.2018.633
AMA SARWAR M , - H , Lİ T . Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1712-1728.
Vancouver SARWAR M , - H , Lİ T . Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1728-1712.