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H. Aydi, Monica-Felicia Bota, E. Karapınar, Slobodan Mitrovic (2012)
A fixed point theorem for set-valued quasi-contractions in b-metric spacesFixed Point Theory and Applications, 2012
A. Eldred, P. Veeramani (2006)
Existence and convergence of best proximity pointsJournal of Mathematical Analysis and Applications, 323
B) ≤ lim k→∞ d(a 2n k , Fa) ≤ d(A, B)
J. Joseph, D. Roselin, M. Marudai (2016)
Fixed point theorems on multi valued mappings in b-metric spacesSpringerPlus, 5
1 + c 2 + c 3 )d(b, Fa) + (1 − (c 1 + c 2 + c 3 ))d(A, B) < d
J Maria Joseph, D Dayana Roselin, M Marudai (2016)
Fixed point theorems on multi valued mappings in $$b$$ b -metric spacesSpringer Plus, 5
M. Al-Thagafi, N. Shahzad (2009)
Convergence and existence results for best proximity pointsNonlinear Analysis-theory Methods & Applications, 70
A. Raj, J. Joseph, M. Marudai (2014)
Theorems On Best Proximity Points For Generalized Rational Proximal Contractions
M. Boriceanu (2009)
FIXED POINT THEORY FOR MULTIVALUED GENERALIZED CONTRACTION ON A SET WITH TWO b-METRICS
J Maria Joseph, M Marudai (2012)
Some results on existence and convergence of best proximity pointsFar East J. Math. Sci., 66
In this paper, we prove best proximity point theorems for types of cyclic b-contrac- tion mappings in the setting of complete b-metric spaces which generalize some results in the current literature. Keywords Fixed point · Best proximity point · Complete metric space · Contraction · b-Metric space Mathematics Subject Classification 46N40 · 47H10 · 54H25 1 Introduction and preliminaries The fixed point theory plays a vital role in mathematical analysis. Best approxima - tions and best proximity points are considered as an extension of fixed point theory. In 1922, Stefan Banach has come up with beautiful theorem known as banach con- traction theorem. This theorem laid foundation for all fixed point theorems. Eldred and Veeramani [1] proved existence and convergence of best proximity points in 2006. Then, many authors presented best proximity point results for different types of mappings [2–5]. In this section, we provide some basic definitions. Define dist(A, B)= inf{d(a, b)∶ a ∈ A, b ∈ B} A ={a ∈ A ∶ d(a, b)= dist(A, B) for some b ∈ B} B ={b ∈ B ∶ d(a, b)= dist(A, B) for some a ∈ A} * J. Maria Joseph joseph80john@gmail.com J. Beny benykutty@gmail.com M. Marudai marudaim@yahoo.co.in Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli 620 002, India Department of Mathematics,
The Journal of Analysis – Springer Journals
Published: Nov 28, 2018
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