Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

Kongban, Chayut

doi:10.1515/fascmath-2017-0019

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“…The contribution of Eldred and Veeramani was to create the cyclic contraction. Many authors have created several different contractions by modifying Eldred and Veeramani; see e.g., [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In this paper, we define a new map which is concerned with the alternative n-sets methodology instead of 2-sets or sequentially n-sets as follows: Definition 3.…”

Section: Introductionmentioning

confidence: 99%

Best Proximity Points for Alternative Maps

Chen¹

2019

Symmetry

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Let ( X , d ) be a metric space and Ω i , i = 1 , 2 , … , m , be a nonempty subset of ( X , d ) . An operator T : ∪ 1 ≤ i ≤ m Ω i → ∪ 1 ≤ i ≤ m Ω i is called an alternative map if T ( Ω j ) ⊆ ∪ i ≠ j Ω i , j = 1 , 2 , … , m . In addition, if for any x, y ∈ ∪ 1 ≤ i ≤ m Ω i , there exists a constant α ∈ [ 0 , 1 ) such that d ( T x , T y ) ≤ α d ( x , y ) + ( 1 − α ) d ( Ω j , Ω k ) for some Ω j and Ω k ∈ { Ω i } i = 1 m with x ∈ Ω j and y ∈ Ω k , then we call T an alternative contraction. Moreover, if ( X , d ) has an alternative UC property and T is an alternative contraction, then the best proximity point of T exists.

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Section: Introductionmentioning

confidence: 99%

Best Proximity Points for Alternative Maps

Chen¹

2019

Symmetry

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“…In 2017, Anh [29] introduced the concept of random best proximity point of a random operator. Thereafter, many authors have focused on various existence theorems of random best proximity point; for detail, see [30][31][32].…”

Section: Introductionmentioning

confidence: 99%