Image restoration via Picard's and Mountain-pass Theorems

Souad Ayadi; Ozgur Ege; Souad Ayadi; Ozgur Ege

doi:10.3934/era.2022055

Electronic Research Archive

2022, Volume 30, Issue 3: 1052-1061. doi: 10.3934/era.2022055

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Research article

Image restoration via Picard's and Mountain-pass Theorems

Souad Ayadi ¹,
Ozgur Ege ^{2
,
,}

1.
Science Department of Matter, Faculty of Science, Djilali Bounaama University, Khemis Miliana, Algeria
2.
Department of Mathematics, Faculty of Science, Ege University, Bornova 35100, Izmir, Turkey

Received: 01 December 2021 Revised: 02 February 2022 Accepted: 20 February 2022 Published: 08 March 2022

In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.
- image restoration,
- fixed point,
- Picard Theorem,
- Mountain-pass Theorem,
- image processing
Citation: Souad Ayadi, Ozgur Ege. Image restoration via Picard's and Mountain-pass Theorems[J]. Electronic Research Archive, 2022, 30(3): 1052-1061. doi: 10.3934/era.2022055

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Abstract

In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.

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