Iterative Schemes Involving Several Mutual Contractions

María A. Navascués (), Sangita Jha, Arya K. B. Chand and Ram N. Mohapatra
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María A. Navascués: Departamento de Matemática Aplicada, Escuela de Ingeniería y Arquitectura, Universidad de Zaragoza, 50018 Zaragoza, Spain
Sangita Jha: Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India
Arya K. B. Chand: Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
Ram N. Mohapatra: Department of Mathematics, University of Central Florida, Orlando, FL 32817, USA

Mathematics, 2023, vol. 11, issue 9, 1-18

Abstract: In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to add a more extended underlying structure. We provide sufficient conditions for two mutually Reich contractive maps in order to have a common fixed point. The result is extended to a family of operators of any cardinality. The dynamics of iterative discrete systems involving this type of self-maps is studied. In the case of normed spaces, we establish some relations between mutual Reich contractivity and classical contractivity for linear operators. Then, we introduce the new concept of mutual functional contractivity that generalizes the concept of classical Banach contraction, and perform a similar study to the Reich case. We also establish some relations between mutual functional contractions and Banach contractivity in the framework of quasinormed spaces and linear mappings. Lastly, we apply the obtained results to convolutional operators that had been defined by the first author acting on Bochner spaces of integrable Banach-valued curves.

Keywords: iteration; fixed point; discrete dynamical systems; attractors; Reich mappings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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