scholarly journals Best Approximation Results in Various Frameworks

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 67
Author(s):  
Taoufik Sabar ◽  
Abdelhafid Bassou ◽  
Mohamed Aamri
Keyword(s):  
Best Approximation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Partial Metric ◽  
Relatively Nonexpansive Mappings ◽  
Partial Metric Spaces ◽  
Relatively Nonexpansive ◽  
Cyclic Mapping

We first provide a best proximity point result for quasi-noncyclic relatively nonexpansive mappings in the setting of dualistic partial metric spaces. Then, those spaces will be endowed with convexity and a result for a cyclic mapping will be obtained. Afterwards, we prove a best proximity point result for tricyclic mappings in the framework of the newly introduced extended partial S b -metric spaces. In this way, we obtain extensions of some results in the literature.

scholarly journals Best Proximity Results on Dualistic Partial Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 306 ◽  
Author(s):  
Ariana Pitea
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Auxiliary Function ◽  
Partial Metric ◽  
Partial Metric Spaces

We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point.

scholarly journals Existence and Convergence Theorems of Best Proximity Points

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Banach Spaces ◽  
Convergence Theorem ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Best Proximity Points ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive

The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.

scholarly journals Some best proximity point results for multivalued mappings on partial metric spaces

2021 ◽  
Vol 25 (1) ◽  
pp. 99-111
Author(s):  
Mustafa Aslantas ◽  
Al-Zuhairi Abed
Keyword(s):  
Contraction Mapping ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Partial Metric ◽  
Multivalued Contraction ◽  
New Concepts ◽  
Partial Metric Spaces

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic Feng-Liu type multivalued contraction mapping. Then, we obtain some new best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, we provide examples to show the effectiveness of our results.

scholarly journals Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1098
Author(s):  
Nilakshi Goswami ◽  
Raju Roy ◽  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Integral Equation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Common Best Proximity Point ◽  
New Class ◽  
Partial Metric Spaces

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

scholarly journals Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Laishram Shanjit ◽  
Yumnam Rohen ◽  
K. Anthony Singh
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Relatively Nonexpansive Mapping ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Mann’S Iteration

In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying T A ⊆ B , T B ⊆ A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively nonexpansive mapping with respect to orbits converges to a fixed point. These relatively nonexpansive mappings with respect to orbits need not be continuous. Some illustrations are given in support of our results.

scholarly journals Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3149-3158 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Normal Structure ◽  
Relatively Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Relatively Nonexpansive ◽  
Cyclic Contractions ◽  
Funct Anal ◽  
Best Proximity Pair

In this article, we formulate a best proximity pair theorem for noncyclic relatively nonexpansive mappings in convex metrc spaces by using a geometric notion of semi-normal structure. In this way, we generalize a corresponding result in [W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142-149]. We also establish a best proximity pair theorem for pointwise noncyclic contractions in the setting of convex metric spaces. Our result generalizes a result due to Sankara Raju Kosuru and Veeramani [G. Sankara Raju Kosuru and P. Veeramani, A note on existence and convergence of best proximity points for pointwise cyclic contractions, Numer. Funct. Anal. Optim., 82 (2011) 821-830].

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