Generalization of Rakotch's fixed Point Theorem

Morales, J. R.

doi:10.15517/rmta.v9i1.207

Cited by 2 publications

(1 citation statement)

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“…A huge number of numerical algorithms and mathematical methods were established by using this principle (for instance, the solution of equations of all types: algebraic, differential, integral). The Banach theorem was extended by many authors to some larger and different classes of contractive mappings; see more details in [1][2][3][4][5][6][7] and the references therein. Here, we introduce two generalizations of the classical (Banach) contraction involving two operators on a metric space instead of a single map.…”

Section: Introductionmentioning

confidence: 99%

Iterative Schemes Involving Several Mutual Contractions

et al. 2023

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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.

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