A global optimality result in probabilistic spaces using control function

Saha, P.; Guria, Shantau; Bhandari, Samir Kumar; Choudhury, Binayak S.

doi:10.1080/02331934.2020.1781118

Cited by 3 publications

(6 citation statements)

References 19 publications

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“…In [15] it is shown that the probabilistic distance between two non-empty subsets M and N is a distribution function. We describe this result along with its proof in the following lemma.…”

Section: Resultsmentioning

confidence: 99%

“…Definition 1.13 [15] Let (M, N ) be a pair of non-empty subsets of a Menger space (S, Γ, ξ). Let h : M → N and τ :…”

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

“…Definition 1.9 [15] Let (S, Γ) be a probabilistic metric space. The probabilistic distance of a point κ ∈ S from a non-empty set M for η > 0 is defined as…”

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

“…Definition 1.10 [15,18] Let M and N be two non-empty subsets of a Menger space (S, Γ, ξ). An element κ * ∈ M is said to be a best proximity point of the mapping h : M → N if it satisfies the condition that for all η > 0,…”

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

“…Fixed point theory has particularly a large literature on this space [3,11]. A best proximity point problem has been discussed on PM-spaces in a recent paper [15] by the present authors.…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

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A Problem in Probabilistic Optimization

Bhandari,

Saha,

Guria

et al. 2023

Preprint

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In our present discussion our target is to describe a method for determining the probabilistic distance between two sets. The approach here is through a construction of a non-self contraction from one set to the other and then seeking a global optimal approximate solution of the corresponding fixed point equation in probabilistic terms where the exact solution does not exist in general. The main theorem is illustrated with an example. The study is in the domain of probabilistic optimization.

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“…In [15] it is shown that the probabilistic distance between two non-empty subsets M and N is a distribution function. We describe this result along with its proof in the following lemma.…”

Section: Resultsmentioning

confidence: 99%

“…Definition 1.13 [15] Let (M, N ) be a pair of non-empty subsets of a Menger space (S, Γ, ξ). Let h : M → N and τ :…”

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

“…Definition 1.9 [15] Let (S, Γ) be a probabilistic metric space. The probabilistic distance of a point κ ∈ S from a non-empty set M for η > 0 is defined as…”

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

Section: Definition 14 Menger Probabilistic Metric Space or Menger Sp...mentioning

confidence: 99%

“…Fixed point theory has particularly a large literature on this space [3,11]. A best proximity point problem has been discussed on PM-spaces in a recent paper [15] by the present authors.…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

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A Problem in Probabilistic Optimization

Bhandari,

Saha,

Guria

et al. 2023

Preprint

Self Cite

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A note on the paper ‘A global optimality result in probabilistic spaces using control function’

Gabeleh

2022

Optimization

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Global optimization problem and probabilistic distance

Bhandari,

De la Sen,

Chandok

2024

IFS

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In this article, the probabilistic metric distance between two disjoint sets is utilised to define the essential criteria for the existence and uniqueness of the best proximity point, which takes into account the global optimization problem. In order to solve this problem, we pretend that we are trying to obtain the optimal approximation to the solution of a fixed point equation. Here, we introduce two types of probabilistic proximal contraction mappings and use a geometric property called Ω-property in the context of probabilistic metric spaces. We also obtain some consequences for self-mappings, which give the fixed point results. Some examples are provided to validate the findings. As an application, we obtain the solution to a second-order boundary value problem using a minimum t-norm in the context of probabilistic metric spaces.

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A global optimality result in probabilistic spaces using control function

Cited by 3 publications

References 19 publications

A Problem in Probabilistic Optimization

A Problem in Probabilistic Optimization

A note on the paper ‘A global optimality result in probabilistic spaces using control function’

Global optimization problem and probabilistic distance

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