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
Primary Language | English |
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Subjects | Mathematics |
Journal Section | Mathematics |
Authors |
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Publication Date | December 8, 2019 |
Published in Issue | Year 2019, Volume 48, Issue 6 |
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}, number = {6}, 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 Li, Tongxing} } |
APA | Sarwar, M. , -, H. & Li, 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. , Li, 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. , Li, 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 Li 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 Li %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 , Li, 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. , Li 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. , Li 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. |
IEEE | M. Sarwar , H. - and T. Li , "Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1712-1728, Dec. 2019, doi:10.15672/HJMS.2018.633 |