Solution of integral equations via new Z-contraction mapping in Gb-metric spaces
Mebawondu, Akindele Adebayo
Oyewole, Kazeem Olawale
Mewomo, Oluwatosin Temitope
We introduce a new type of (?, ?)-admissibility and (?, ?)-Z-contraction mappings in the frame work of Gb-metric spaces. Using these concepts, fixed point results for (?, ?)-Z-contraction mappings in the frame work of complete Gb-metric spaces are established. As an application, we discuss the existence of solution for integral equation of the form: x(t) = g(t) + ?10 K(t, s, u(s))ds, t ? [0, 1], O. T. Mewomowhere K : [0, 1]×[0, 1]×R ? R and g : [0, 1] ? R are continuous functions. The results obtained in this paper generalize, unify and improve the results of Liu et al., , Antonio-Francisco et al. , Khojasteh et al. , Kumar et al.  and others in this direction.