Fixed Point Theorems for Expansive Mapping in
𝑨-Metric Space

Parkhey, Bhawna; Daheriya, R. D.; Ughade, Manoj

doi:10.29055/jcms/853

Cited by 2 publications

(3 citation statements)

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“…But a b-metric is not necessarily a Strong Altering JS-metric. The function defined by 𝐽 𝜙 (𝑗, 𝑝) = (𝑗 − 𝑝) 2 , is a b-metric and also an Altering JS-metric but not a Strong Altering JSmetric. It is observed that the Strong Altering JSmetric compresses the distance whereas a b-metric magnifies it.…”

Section: Proposition 2: Any Metric Space Is a Strongmentioning

confidence: 99%

“…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%

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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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Section: Proposition 2: Any Metric Space Is a Strongmentioning

confidence: 99%

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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“…Definition 4 ([23]). Tx = x is the fixed point of mapping; the set T X → X into itself is for every x that is mapped into itself [23].…”

Section: Fractional Black-scholes Equation and Contractive Mappingmentioning

confidence: 99%

A New Solution to the Fractional Black–Scholes Equation Using the Daftardar-Gejji Method

Sugandha,

Rusyaman,

Sukono

et al. 2023

Mathematics

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The main objective of this study is to determine the existence and uniqueness of solutions to the fractional Black–Scholes equation. The solution to the fractional Black–Scholes equation is expressed as an infinite series of converging Mittag-Leffler functions. The method used to discover the new solution to the fractional Black–Scholes equation was the Daftardar-Geiji method. Additionally, the Picard–Lindelöf theorem was utilized for the existence and uniqueness of its solution. The fractional derivative employed was the Caputo operator. The search for a solution to the fractional Black–Scholes equation was essential due to the Black–Scholes equation’s assumptions, which imposed relatively tight constraints. These included assumptions of a perfect market, a constant value of the risk-free interest rate and volatility, the absence of dividends, and a normal log distribution of stock price dynamics. However, these assumptions did not accurately reflect market realities. Therefore, it was necessary to formulate a model, particularly regarding the fractional Black–Scholes equation, which represented more market realities. The results obtained in this paper guaranteed the existence and uniqueness of solutions to the fractional Black–Scholes equation, approximate solutions to the fractional Black–Scholes equation, and very small solution errors when compared to the Black–Scholes equation. The novelty of this article is the use of the Daftardar-Geiji method to solve the fractional Black–Scholes equation, guaranteeing the existence and uniqueness of the solution to the fractional Black–Scholes equation, which has not been discussed by other researchers. So, based on this novelty, the Daftardar-Geiji method is a simple and effective method for solving the fractional Black–Scholes equation. This article presents some examples to demonstrate the application of the Daftardar-Gejji method in solving specific problems.

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Fixed Point Theorems for Expansive Mapping in 𝑨-Metric Space

Cited by 2 publications

References 0 publications

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

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

A New Solution to the Fractional Black–Scholes Equation Using the Daftardar-Gejji Method

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