3D analysis of modified <i>F</i>-contractions in convex b-metric spaces with application to Fredholm integral equations

Awais Asif; Sami Ullah Khan; Thabet Abdeljawad; Muhammad Arshad; Ekrem Savas; Awais Asif; Sami Ullah Khan; Thabet Abdeljawad; Muhammad Arshad; Ekrem Savas

doi:10.3934/math.2020444

AIMS Mathematics

2020, Volume 5, Issue 6: 6929-6948. doi: 10.3934/math.2020444

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Research article

3D analysis of modified F-contractions in convex b-metric spaces with application to Fredholm integral equations

1.
Department of Math & Stats, International Islamic University Islamabad, Pakistan
2.
Department of Mathematics, Gomal University, D. I. Khan, 29050, KPK, Pakistan
3.
Department of Mathematics and General Sciences, Prince Sultan University, P.O Box 66833, Riyadh
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
6.
Department of Mathematics, Usak University, Turkey

Received: 21 April 2020 Accepted: 26 August 2020 Published: 08 September 2020
MSC : 54H25

The article defines F-Reich contraction while eliminating the condition (F3) and (F4) of F-contraction of Nadler type defined by Cosentino and using generalized Mann's iteration algorithm, some interesting theorems are developed in the setting of convex b-metric spaces. Example are stated in support of our proved results and application of our results in finding solution point to Fredholm Integral equation of the second kind are given.
- convex structure,
- convex b-metric space,
- Mann's iteration,
- Fredholm integral equation,
- F-Reich contraction
Citation: Awais Asif, Sami Ullah Khan, Thabet Abdeljawad, Muhammad Arshad, Ekrem Savas. 3D analysis of modified F-contractions in convex b-metric spaces with application to Fredholm integral equations[J]. AIMS Mathematics, 2020, 5(6): 6929-6948. doi: 10.3934/math.2020444

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Abstract

The article defines F-Reich contraction while eliminating the condition (F3) and (F4) of F-contraction of Nadler type defined by Cosentino and using generalized Mann's iteration algorithm, some interesting theorems are developed in the setting of convex b-metric spaces. Example are stated in support of our proved results and application of our results in finding solution point to Fredholm Integral equation of the second kind are given.

References

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