Best proximity points, cyclic Kannan maps and geodesic metric spaces

Abstract In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We take two different approaches, each one leading to different results that complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.

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Existence and uniqueness of best proximity points in geodesic metric spaces

Nonlinear Analysis ◽

10.1016/j.na.2010.04.005 ◽

2010 ◽

Vol 73 (4) ◽

pp. 915-921 ◽

Cited By ~ 15

Author(s):

Aurora Fernández-León

Keyword(s):

Existence And Uniqueness ◽

Metric Spaces ◽

Best Proximity Points ◽

Geodesic Metric

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Tripartite Coincidence-Best Proximity Points and Convexity in Generalized Metric Spaces

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-019-00137-0 ◽

2019 ◽

Vol 50 (4) ◽

pp. 999-1028 ◽

Cited By ~ 1

Author(s):

M. Norouzian ◽

A. Abkar

Keyword(s):

Metric Spaces ◽

Generalized Metric Spaces ◽

Best Proximity Points ◽

Generalized Metric

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

Fasciculi Mathematici ◽

10.1515/fascmath-2017-0019 ◽

2017 ◽

Vol 59 (1) ◽

pp. 91-105 ◽

Cited By ~ 2

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].

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BEST PROXIMITY POINTS AND FIXED POINTS WITH -FUNCTIONS IN THE FRAMEWORK OF -DISTANCES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718001193 ◽

2018 ◽

Vol 99 (03) ◽

pp. 497-507 ◽

Cited By ~ 1

Author(s):

ALEKSANDAR KOSTIĆ ◽

ERDAL KARAPINAR ◽

VLADIMIR RAKOČEVIĆ

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Best Proximity Points

We study best proximity points in the framework of metric spaces with $w$ -distances. The results extend, generalise and unify several well-known fixed point results in the literature.

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On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

Discrete Dynamics in Nature and Society ◽

10.1155/2016/4186960 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

M. De la Sen

Keyword(s):

Fixed Points ◽

Metric Spaces ◽

Nonempty Intersection ◽

Generalized Metric Spaces ◽

Best Proximity Points ◽

Generalized Metric ◽

Cyclic Maps ◽

Convergence Of Sequences ◽

Composite Maps ◽

Decreasing Functions

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-calledr-weaker Meir-Keeler orr,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.

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On Best Proximity Points of Generalized Almost-F-Contraction Mappings

Journal of the Indonesian Mathematical Society ◽

10.22342/jims.25.1.532.16-23 ◽

2019 ◽

Vol 25 (1) ◽

pp. 16-23

Author(s):

Mahdi Salamatbakhsh ◽

Robab Hamlbarani Haghi

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Best Proximity Points ◽

Contraction Mappings

We provide some results about best proximity points of generalized almost-$F$-contraction mappings in metric spaces which generalize and extend recent fixed point theorems. Also, we give an example to illustrate our main result.

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