Fixed points of non-linear multivalued graphic contractions with applications

Mohammed Shehu Shagari; Trad Alotaibi; Hassen Aydi; Choonkil Park; Mohammed Shehu Shagari; Trad Alotaibi; Hassen Aydi; Choonkil Park

doi:10.3934/math.20221103

AIMS Mathematics

2022, Volume 7, Issue 11: 20164-20177. doi: 10.3934/math.20221103

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Fixed points of non-linear multivalued graphic contractions with applications

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics, Taif University, Taif, 21944, Saudi Arabia
3.
Institut Superieur d Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
4.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
6.
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea

Received: 13 April 2022 Revised: 24 August 2022 Accepted: 31 August 2022 Published: 14 September 2022
MSC : 47H10, 54H25, 47H04

In this paper, a novel and more general type of sequence of non-linear multivalued mappings as well as the corresponding contractions on a metric space equipped with a graph is initiated. Fixed point results of a single-valued mapping and the new sequence of multivalued mappings are examined under suitable conditions. A non-trivial comparative illustration is provided to support the assumptions of our main theorem. A few important results in $ \epsilon $-chainable metric space and cyclic contractions are deduced as some consequences of the concepts obtained herein. As a result of our findings, new criteria for solving a broader form of Fredholm integral equation are established. An open problem concerning discretized population balance model whose solution may be investigated using any of the ideas proposed in this note is highlighted as a future assignment.
- fixed point,
- non-linear multivalued graphic contraction,
- coincidence point,
- sequence of multivalued maps
Citation: Mohammed Shehu Shagari, Trad Alotaibi, Hassen Aydi, Choonkil Park. Fixed points of non-linear multivalued graphic contractions with applications[J]. AIMS Mathematics, 2022, 7(11): 20164-20177. doi: 10.3934/math.20221103

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Abstract

In this paper, a novel and more general type of sequence of non-linear multivalued mappings as well as the corresponding contractions on a metric space equipped with a graph is initiated. Fixed point results of a single-valued mapping and the new sequence of multivalued mappings are examined under suitable conditions. A non-trivial comparative illustration is provided to support the assumptions of our main theorem. A few important results in $ \epsilon $-chainable metric space and cyclic contractions are deduced as some consequences of the concepts obtained herein. As a result of our findings, new criteria for solving a broader form of Fredholm integral equation are established. An open problem concerning discretized population balance model whose solution may be investigated using any of the ideas proposed in this note is highlighted as a future assignment.

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