Fixed Point Results of Expansive Mappings in Metric Spaces

Yeşilkaya, Seher Sultan; Aydın, Cafer

doi:10.3390/math8101800

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Yeilkaya and Aydin [2] gave a good account and in depth analysis of expansive mapping, efforts can be directed towards the existence of fixed point in expansive mappings.…”

Section: Types Of Expansive Mappingsmentioning

confidence: 99%

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Vincent¹,

Sammy²,

Jeremiah³

2023

ARJOM

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Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

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“…Yeilkaya and Aydin [2] gave a good account and in depth analysis of expansive mapping, efforts can be directed towards the existence of fixed point in expansive mappings.…”

Section: Types Of Expansive Mappingsmentioning

confidence: 99%

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Vincent¹,

Sammy²,

Jeremiah³

2023

ARJOM

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“…Most importantly it plays a key role in fixed point theory. Wang et al 1 examined the fixed-point results using Expansive type mappings in their paper in 1984 which motivated several researchers to study the expansive mappings [2][3][4][5] in various extensions of metric spaces. Dislocated metric space explored by Hitzler and Seda 6 in 2000 and the b-metric space initiated by Bhaktin 7 and Czerwik 8 independently are some notable generalized metric spaces available in the literature.…”

Section: Introductionmentioning

confidence: 99%

Existence of Fixed Points for Expansive Mappings in Complete Strong Altering JS-metric space

VARUNNYA

Gnanachandra²,

ANANDAPRIYA³

2023

Baghdad Sci.J

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The paper aims at initiating and exploring the concept of extended metric known as the Strong Altering JS-metric, a stronger version of the Altering JS-metric. The interrelation of Strong Altering JS-metric with the b-metric and dislocated metric has been analyzed and some examples have been provided. Certain theorems on fixed points for expansive self-mappings in the setting of complete Strong Altering JS-metric space have also been discussed.

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Applications of some new Krasnoselskii-type fixed-point results for generalized expansive and equiexpansive mappings

2022

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We consider Ω as a subset of a Banach space W and Λ as a function of Ω into W. Let Ϝ be a function whose image values lie in W and domain is $\Lambda (\Omega )\times \Omega $ Λ ( Ω ) × Ω or $\Omega \times \Omega $ Ω × Ω . In this paper, we establish some fixed-point results for a generalized expansive and equiexpansive operator Ϝ such that $\Omega \subseteq \digamma (\Lambda \omega ,\Omega )$ Ω ⊆ Ϝ ( Λ ω , Ω ) or $\Omega \subseteq \digamma (\omega ,\Omega )$ Ω ⊆ Ϝ ( ω , Ω ) . We apply our results to acquire the solutions of fractional evolution equations and certain types of integral equations. We demonstrate our results with examples, and plot approximate and exact solutions with errors.

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Fixed Point Results of Expansive Mappings in Metric Spaces

Cited by 3 publications

References 12 publications

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Derivation of Fixed-Point Theorem Using Expansive Mapping Approach

Existence of Fixed Points for Expansive Mappings in Complete Strong Altering JS-metric space

Applications of some new Krasnoselskii-type fixed-point results for generalized expansive and equiexpansive mappings

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