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

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-05-0078

Keywords:

(α, β)-ZF –contraction, (α, β)-admissible type B mapping, Fixed point; Gb-metric space

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.

Author Biographies

Akindele Adebayo Mebawondu, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (MaSS)

Chinedu Izuchukwu, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (MaSS).

Kazeem Olawale Oyewole, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (MaSS).

Oluwatosin Temitope Mewomo, University of KwaZulu-Natal.

School of Mathematics, Statistics and Computer Science, DST.

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Published

2020-10-01

How to Cite

[1]
A. A. Mebawondu, C. Izuchukwu, K. O. Oyewole, and O. T. Mewomo, “Solution of integral equations via new Z-contraction mapping in Gb-metric spaces”, Proyecciones (Antofagasta, On line), vol. 39, no. 5, pp. 1273-1294, Oct. 2020.

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