Generalized suzuki-type mappings in modular vector spaces

Bejenaru, Andreea; Postolache, Mihai

doi:10.1080/02331934.2019.1647202

Cited by 4 publications

(6 citation statements)

References 14 publications

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“…Condition (E) is wider than Suzuki's condition but stronger than quasi-nonexpansiveness. Another extension was subject to analysis in [19]. However, these generalized properties will not be a topic to be approached in this survey.…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

Usurelu

Postolache

2019

Symmetry

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The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property ( C ) holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of R 2 with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence.

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Section: Introductionmentioning

confidence: 99%

Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

Usurelu

Postolache

2019

Symmetry

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“…Definition 12. (See [3].) Let ρ be a convex modular satisfying ∆ 2 -condition on a vector space X, and let S ⊂ X ρ be a nonempty subset.…”

Section: M1 Condition (ρC) or Modular Suzuki Nonexpansive Mappingsmentioning

confidence: 99%

“…The idea of looking for new contractive conditions to lead to wider and wider classes of mappings, as well as the effort of extending the metric setting, are two of the main directions in fixed point theory. This paper provides a new contribution related to these directions by defining a new nonexpansiveness property, on Banach spaces initially, and extending it afterwards to modular vector spaces (please see [11,12] for the definition of modular vector spaces, as well as [1][2][3][4][5][8][9][10] and others, for important properties and connections with fixed point theory).…”

Section: Introductionmentioning

confidence: 99%

“…• Condition (C) in [4] as a modular extension of the Suzuki's nonexpansiveness property; • The modular Suzuki-type generalized nonexpansive mappings in [3] as a modular extension for the mappings defined in [13], as well as generalization for mappings satisfying condition (ρC); • Condition (ρE) in [8], i.e. the modular version of condition (E).…”

Section: Introductionmentioning

confidence: 99%

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A unifying approach for some nonexpansiveness conditions on modular vector spaces

Bejenaru

Postolache

2020

NAMC

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This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

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“…Lately, various modular structures, viewed as alternatives to classical normed or metric spaces, have been intensely studied in connection with the fixed point theory. Many modular related research papers adopted the setting of a modular vector space (see [1][2][3][4][5]), while others used the more general framework of a metric modular space (see [6][7][8][9][10][11]). The notion of a metric modular, together with its stronger convex version, was firstly introduced and studied by Chistyakov in [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

Kassab

2019

Symmetry

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This paper introduces two new contractive conditions in the setting of non-Archimedean modular spaces, via a C-class function, an altering distance function, and a control function. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. The main outcomes provide sufficient conditions for the existence of common fixed points for four mappings. Examples are provided in order to prove the usability of the theoretical approach. Moreover, these examples use a non-Archimedean metric modular, which is not convex, making the study of nonconvex modulars more appealing.

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Generalized suzuki-type mappings in modular vector spaces

Cited by 4 publications

References 14 publications

Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

A unifying approach for some nonexpansiveness conditions on modular vector spaces

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

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