Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

Karapınar, Erdal; Agarwal, Ravi P.; Aydi, Hassen

doi:10.3390/math6110256

Cited by 116 publications

(75 citation statements)

References 13 publications

(22 reference statements)

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“…Furthermore, for the different examples of simulation functions (as we showed in Theorems 5 and 6), one can get more new corollaries. Lastly, by regarding hybrid contraction approaches, one can get several more consequences, by following the techniques in [21,[24][25][26].…”

Section: Discussionmentioning

confidence: 99%

Admissible Hybrid Z-Contractions in b-Metric Spaces

Chifu

Karapınar

2019

Axioms

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In this manuscript, we introduce a new notion, admissible hybrid Z-contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam-Hyers stability of the fixed point problem are also studied.Axioms 2020, 9, 2 2 of 17As it was mentioned before, the theory has been advanced by reporting several new fixed point results that are obtained by changing the conditions on the given mappings. As a result, in the literature, there are so many different types of metric fixed point results that cause a disturbance, conflict, and disorder. For overcoming this problem, it needs to consider new theorems that cover several different results. One of the successful results in directions was given in [4] where admissible mappings were introduced to combine different structures. Other interesting results were given in [5] in which the notion of the simulation function was defined to combine many distinct contractions. The notion of the hybrid contractions can also be considered as a result of this trend: in two recent papers [6,7], the authors introduce a new type of contraction, namely admissible hybrid contraction, in order to unify several linear, nonlinear and interpolative contractions in the set-up of a complete metric and b-metric spaces.One of the main aims of this paper is to unify the several existing results in the literature by combining the interesting notions: admissible mappings, simulation functions, and hybrid contractions. Besides unifying the results, we express our results in the most generalized form: in the setting of a complete b-metric space. Next, we shall consider applications for our obtained results. In particular, we shall consider the well-posedness and the Ulam-Hyers stability of the fixed point problem. We shall give some consequences and we shall indicate how one can get more consequences from the main theorem of the paper. In the next section, we shall give some basic notions and results to provide a self-contained, easily readable paper. PreliminariesIn this section, we shall collect the necessary notations, notions, and results for the sake of the completeness of the paper. We first express the definition of the b-metric, as follows.Definition 1 (See, e.g., Bourbaki [1], Bakhtin [2], and Czerwik [3]). Let X be a nonempty set and let s ≥ 1 be a given real number. A functional d : X × X → [0, ∞) is said to be a b-metric with constant s, if

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Section: Discussionmentioning

confidence: 99%

Admissible Hybrid Z-Contractions in b-Metric Spaces

Chifu

Karapınar

2019

Axioms

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“…for all k ≥ n 1 . Letting n, m → ∞ in the inequality above, and keeping in mind the observations in (16), (30), (25), (28) and (29), we find that…”

Section: Resultsmentioning

confidence: 53%

Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions

Karapınar

Agarwal

2019

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Karapinar [9] defined the generalized Kannan-type contraction by adopting the interpolative approach in the following manner, and proved that such an interpolative Kannan-type contraction owns a fixed point in a complete metric space. Some more interesting results in this direction may be found in the work of Karapinar et al [10,11].…”

Section: Introductionmentioning

confidence: 82%

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

Debnath

Sen

2019

Symmetry

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The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk-Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modifiedĆirić-Reich-Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for ω-interpolativeĆirić-Reich-Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.

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Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

Cited by 116 publications

References 13 publications

Admissible Hybrid Z-Contractions in b-Metric Spaces

Admissible Hybrid Z-Contractions in b-Metric Spaces

Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

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