Existence and uniqueness integral equations in C*-algebra-valued $s_b$-metric spaces by some coupled fixed point theorems


Seyede Samira Razavi, Hashem Parvaneh Masiha




We study some coupled fixed point theorems in C*-algebra-valued $S_b$-metric spaces. As applications, existence and uniqueness results for one type of integral equation \[ x(t)=ıt_E(K_1(t,s)+K_2(t,s))(f(s,x(s))+g(s,x(s)))ds+h(t),\quad tı E \] where $E$ is the Lebesque measurable set and $m(E)<+\infty$, and under some other conditions are given.