Solving the system of nonlinear integral equations via rational contractions

Kumara Swamy Kalla; Sumati Kumari Panda; Thabet Abdeljawad; Aiman Mukheimer; Kumara Swamy Kalla; Sumati Kumari Panda; Thabet Abdeljawad; Aiman Mukheimer

doi:10.3934/math.2021212

AIMS Mathematics

2021, Volume 6, Issue 4: 3562-3582. doi: 10.3934/math.2021212

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Research article

Solving the system of nonlinear integral equations via rational contractions

1.
Department of Mathematics, GMR Institute of Technology, Rajam - 532 127, Andhra Pradesh, India
2.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

Received: 22 October 2020 Accepted: 11 January 2021 Published: 21 January 2021
MSC : 54H25

In this paper, some coupled coincidence point theorems for two mappings established using rational type contractions in the setting of partially ordered $ \mathscr{G}- $metric spaces. Moreover, supporting examples are provided to strengthen our obtained results. By considering $ \mathscr{G}- $metric space, we propose a fairly simple solution for a system of nonlinear integral equations by using fixed point technique.
Citation: Kumara Swamy Kalla, Sumati Kumari Panda, Thabet Abdeljawad, Aiman Mukheimer. Solving the system of nonlinear integral equations via rational contractions[J]. AIMS Mathematics, 2021, 6(4): 3562-3582. doi: 10.3934/math.2021212

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Abstract

In this paper, some coupled coincidence point theorems for two mappings established using rational type contractions in the setting of partially ordered $ \mathscr{G}- $metric spaces. Moreover, supporting examples are provided to strengthen our obtained results. By considering $ \mathscr{G}- $metric space, we propose a fairly simple solution for a system of nonlinear integral equations by using fixed point technique.

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