scholarly journals Existence of common best proximity point for single and multivalued non-self mappings

2021 ◽  
Vol 37 (2) ◽  
pp. 273-285
Author(s):  
V. PRAGADEESWARAR ◽  
R. GOPI
Keyword(s):  
Coincidence Point ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Sufficient Condition ◽  
Common Best Proximity Point

In this article, we introduce a new concept called proximal E. A property for single and multivalued mappings. We prove existence of proximally coincidence point for such class of mappings. We provide interesting example which illustrates our main results. Finally, we provide sufficient condition for existence of common best proximity point for this class of mappings.

scholarly journals Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 102 ◽  
Author(s):  
Pradip Debnath ◽  
Hari Mohan Srivastava
Keyword(s):  
Global Optimization ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Best Proximity Points ◽  
Common Best Proximity Point

In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their common best proximity point. Next, we put forward the concept of multivalued Kannan-type contractive pair and also the concept of weak Δ-property to determine the existence of common best proximity point for such a pair of maps.

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3459-3471
Author(s):  
A.H. Ansari ◽  
Geno Jacob ◽  
D. Chellapillai
Keyword(s):  
Best Proximity Point ◽  
Upper Class ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Common Best Proximity Point

In this paper, using the concept of C-class and Upper class functions we prove the existence of unique common best proximity point. Our main result generalizes results of Kumam et al. [[17]] and Parvaneh et al. [[21]].

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 Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

scholarly journals C*-Algebra Valued Fuzzy Soft Metric Spaces and Results for Hybrid Pair of Mappings

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 99
Author(s):  
Ram Daripally ◽  
Naveen Gajula ◽  
Hüseyin Işık ◽  
Srinuvasa Bagathi ◽  
Adi Gorantla
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Multivalued Mappings ◽  
C Algebra ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

In this paper, we establish some results on coincidence point and common fixed point theorems for a hybrid pair of single valued and multivalued mappings in complete C * -algebra valued fuzzy soft metric spaces. In addition, we provided some coupled fixed point theorems. Finally, we have given examples which support our main results.

scholarly journals Proximally Compatible Mappings and Common Best Proximity Points

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 353 ◽  
Author(s):  
V. Pragadeeswarar ◽  
R. Gopi ◽  
M. De la Sen ◽  
Stojan Radenović
Keyword(s):  
Best Proximity Point ◽  
Compatible Mappings ◽  
Best Proximity Points ◽  
Common Best Proximity Point

The purpose of this paper is to introduce and analyze a new idea of proximally compatible mappings and we extend some results of Jungck via proximally compatible mappings. Furthermore, we obtain common best proximity point theorems for proximally compatible mappings through two different ways of construction of sequences. In addition, we provide an example to support our main result.

New hybrid algorithms for global minimization of common best proximity points of some generalized nonexpansive mappings

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2381-2391
Author(s):  
Jenwit Puangpee ◽  
Suthep Suantai
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Best Proximity Point ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Hybrid Algorithms ◽  
Global Minimization ◽  
Numerical Examples ◽  
Common Best Proximity Point ◽  
Two Hybrid

In this paper, we introduce two hybrid algorithms for finding a common best proximity point of two best proximally nonexpansive mappings. We establish strong convergence theorems of the proposed algorithms under some control conditions in a real Hilbert space. Moreover, some numerical examples are given for supporting our main theorems.

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