Solution of integral equations via new Z-contraction mapping in Gb-metric spaces

Abstract

We introduce a new type of (α, β)-admissibility and (α, β)-Z-contraction mappings in the frame work of G b -metric spaces. Using these concepts, fixed point results for (α, β)-Z-contraction mappings in the frame work of complete G b -metric spaces are established. As an application, we discuss the existence of solution for integral equation of the form: x(t) = g(t) + ∫ 1 0 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., [17], Antonio-Francisco et al. [23], Khojasteh et al. [15], Kumar et al. [16] and others in this direction.