Fixed point theory of cyclic operators

Pačurar, Mădălina; Rus, İoan A.

doi:10.1007/s11784-022-00996-z

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Definition 31 ([21]1

Introduction1

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2023

2024

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Cited by 2 publications

(2 citation statements)

References 22 publications

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“…The following simple example, included also in [17], will lead to an important remark regarding the notation used in the above definition.…”

Section: Definition 31 ([21]mentioning

confidence: 99%

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Synchronous r-cyclic contractions on metric spaces

Mădălina

2023

FPT-RO

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Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the r-cyclic operators with respect to a covering of a metric space and investigate their behavior. We study the convergence of the Picard iteration to a fixed point of such an operator under a Banach type generalized contraction condition. The obtained results may have interesting practical applications in various research areas.

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“…The following simple example, included also in [17], will lead to an important remark regarding the notation used in the above definition.…”

Section: Definition 31 ([21]mentioning

confidence: 99%

“…Since then many classes of cyclic operators have been studied, generally by extending known classes of generalized contractions on metric or Banach spaces (see for example [1], [4]- [8], [11]- [14], [18], [22], for a very short list of them).…”

Section: Introductionmentioning

confidence: 99%

Synchronous r-cyclic contractions on metric spaces

Mădălina

2023

FPT-RO

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Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation

Rus

2024

Stud. Univ. Babes-Bolyai Math.

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Let (X, d) be a metric space, f : X → X be a mapping and G(·, f (·)) be an admissible perturbation of f. In this paper we study the following problems: In which conditions imposed on f and G we have the following: (DDE) data dependence estimate for the mapping f perturbation; (UH) Ulam-Hyers stability for the equation, x = f (x); (WP) well-posedness of the fixed-point problem for f; (OP) Ostrowski property of the mapping f. Some research directions are suggested. Mathematics Subject Classification (2010): 47H25, 54H25, 47H09, 65J15, 37N30, 39A30. Received 22 October 2023; Accepted 16 November 2023

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Fixed point theory of cyclic operators

Cited by 2 publications

References 22 publications

Synchronous r-cyclic contractions on metric spaces

Synchronous r-cyclic contractions on metric spaces

Weakly Picard mappings: Retraction-displacement condition, quasicontraction notion and weakly Picard admissible perturbation

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