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

Author
Mebawondu, Akindele Adebayo

Izuchukwu, Chinedu

Oyewole, Kazeem Olawale

Mewomo, Oluwatosin Temitope

Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3586
10.22199/issn.0717-6279-2020-05-0078
Abstract
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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Artes, Arquitectura y UrbanismoCiencias Agrarias, Forestales y VeterinariasCiencias Exactas y NaturalesCiencias SocialesDerechoEconomía y AdministraciónFilosofía y HumanidadesIngenieríaMedicinaMultidisciplinarias
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Universidad de ChileUniversidad Católica de ChileUniversidad de Santiago de ChileUniversidad de ConcepciónUniversidad Austral de ChileUniversidad Católica de ValparaísoUniversidad del Bio BioUniversidad de ValparaísoUniversidad Católica del Nortemore

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