In this paper, taking into account the concepts of startpoint and endpoint we introduce two new definitions including these concepts. Then, we show the relationship between a best proximity point and our new notions with an example. Finally, we prove some results for multivalued mappings on quasi metric spaces.

1.
I.
Altun
,
M.
Aslantas
,
H.
Sahin
, “
Best proximity point results for p-proximal contractions
,”
Acta Mathematica Hungarica.
162
, (
2020
).
2.
M.
Aslantas
, “
Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces
,”
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
70
, (
2021
).
3.
S. S.
Basha
and
P.
Veeramani
, “
Best approximations and best proximity pairs
,”
Acta Sci. Math.
63
, (
1997
).
4.
Y. U.
Gaba
, “
Startpoints and (α, γ)-contractions in quasipseudometric spaces
,”
Journal of Mathematics.
2014
,
2014
.
5.
V. S.
Raj
, “
Best proximity point theorems for non-self mappings
,”
Fixed Point Theory.
14
, (
2013
).
6.
H.
Sahin
, “
Best proximity point theory on vector metric spaces
,”
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
70
, (
2021
).
7.
H.
Sahin
and
D.
Turkoglu
, “
Some Ćirić type periodic point results with Q-function on quasi metric spaces
,” In
AIP Conference Proceedings.
2334
, (
2021
).
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