Best Proximity Points

Veeramani, P.; Shrivastava, Rajesh

doi:10.1007/978-81-322-1883-8_1

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…BPP theory plays an important role in approximating many problems, especially in the fields of differential equations and integral equations. For more details, one can see [24][25][26]. In this section, we obtain the optimum solution of system of differential equations by applying our obtained results.…”

Section: Applications To Differential Equationsmentioning

confidence: 99%

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

2023

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This paper deals with the existence of an optimum solution of a system of ordinary differential equations via the best proximity points. In order to obtain the optimum solution, we have developed the best proximity point results for generalized multivalued contractions of b-metric spaces. Examples are given to illustrate the main results and to show that the new results are the proper generalization of some existing results in the literature.

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Section: Applications To Differential Equationsmentioning

confidence: 99%

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

2023

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“…For a recent account of the theory we refer the reader to [4][5][6]. We can also find in ( [7], pp. 27-31) an application of a best proximity point theorem to a system of differential equations.…”

Section: Introductionmentioning

confidence: 97%

Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces

Chaira

Kabil

Kamouss

et al. 2019

Axioms

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“…One can easily see that a cyclic map is a special case of an alternative map. Due to Fan [4], many authors publish their papers with their Best Proximity Points in [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]:…”

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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Best Proximity Points

Cited by 3 publications

References 25 publications

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

Best Proximity Points for Monotone Relatively Nonexpansive Mappings in Ordered Banach Spaces

Best Proximity Points for Alternative Maps

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