scholarly journals On the existence of coupled best proximity point and best proximity point for Suzuki type alpha^+-theta-proximal multivalued mappings

2017 ◽  
Vol 10 (04) ◽  
pp. 1801-1819 ◽  
Author(s):  
Haiming Liu ◽  
Xiaoming Fan ◽  
Lixu Yan ◽  
Zhigang Wang
Keyword(s):  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Coupled Best Proximity Point

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

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

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 Best Proximity Point Theorems for Single and Multivalued Mappings in Fuzzy Multiplicative Metric Space

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Misbah Farheen ◽  
Tayyab Kamran ◽  
Azhar Hussain
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Best Proximity Point ◽  
Fuzzy Metric Space ◽  
Multivalued Mappings ◽  
Proximal Contraction ◽  
Fuzzy Metric ◽  
Multiplicative Metric Space

In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.

scholarly journals Best Proximity Point forα-ψ-Proximal Contractive Multimaps

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Muhammad Usman Ali ◽  
Tayyab Kamran ◽  
Naseer Shahzad
Keyword(s):  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Multivalued Maps ◽  
Proximal Contraction

We extend the notions ofα-ψ-proximal contraction andα-proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results.

scholarly journals Optimal solutions and applications to nonlinear matrix and integral equations via simulation function

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6087-6106 ◽  
Author(s):  
Azhar Hussain ◽  
Tanzeela Kanwal ◽  
Zoran Mitrovic ◽  
Stojan Radenovic
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Optimal Solutions ◽  
Simulation Function ◽  
Nonlinear Matrix Equation ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
The Given ◽  
Coupled Best Proximity Point ◽  
Definite Solution

Based on the concepts of ?-proximal admissible mappings and simulation function, we establish some best proximity point and coupled best proximity point results in the context of b-complete b-metric spaces. We also provide some concrete examples to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear integral equation and positive definite solution of nonlinear matrix equation X = Q + ?m,i=1 A*i?(X)Ai-?m,i=1 B*i(X)Bi. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

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