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

• Autores: Akindele Adebayo Mebawondu, Chinedu Izuchukwu, Kazeem Olawale Oyewole, Oluwatosin Temitope Mewomo
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 5, 2020, págs. 1273-1294
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-05-0078
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• Resumen

  • 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., [19], Antonio-Francisco et al. [25], Khojasteh et al. [16], Kumar et al. [18] and others in this direction.

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