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

Authors : Muhammad SARWAR, Humaira, Tongxing Lİ

Pages : 1712-1728

Doi:10.15672/HJMS.2018.633

View : 21 | Download : 7

Publication Date : 2019-12-08

Article Type : Research Paper

Abstract :The main purpose of this article is to discuss the existence of the common solution of second-order nonlinear boundary value problems $$\mathfrak{x}``insert ignore into journalissuearticles values(\jmath);=\Bbbkinsert ignore into journalissuearticles values(\jmath,\mathfrak{x}insert ignore into journalissuearticles values(\jmath);,\mathfrak{x}`insert ignore into journalissuearticles values(\jmath););,\quad\text{if}\:\jmath\in[0,\Lambda],\quad\Lambda>0,$$ $$\mathfrak{x}insert ignore into journalissuearticles values(\jmath_1);=\mathfrak{x}_1,\quad\mathfrak{x}insert ignore into journalissuearticles values(\jmath_2);=\mathfrak{x}_2,\quad\jmath_1,\jmath_2\in[0,\Lambda]$$ where $\Bbbk:[0,\Lambda]\times\mathfrak{S}insert ignore into journalissuearticles values(\mathcal{S});\times\mathfrak{S}insert ignore into journalissuearticles values(\mathcal{S});\rightarrow\mathfrak{S}insert ignore into journalissuearticles values(\mathcal{S});$ is a continuous function and $\mathfrak{S}insert ignore into journalissuearticles values(\mathcal{S});$ 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.
Keywords : Complex valued metric space, Fuzzy mapping, Fixed point, Common fixed point, Cauchy sequence, Contractive condition