نویسندگان :
اکرم صفری هفشجانی ( دانشگاه پیام نور )
چکیده
Let $A$ and $B$ be nonempty subsets of a metric space $(X,d)$ and self mapping $T:Acup B o Acup B$ be a cyclic map.
In 2013 Amini-Harandi [`Best proximity point theorems for cyclic strongly quasi-contraction mappings , J. Global Optim. 56 (2013), 1667-1674] introduced the
notion of maps called cyclic strongly quasi-contraction, with adding the condition
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egin{align}label{I0}
d(T^2x,T^2y) leq c~d(x, y)+(1-c)d(A,B)
onumber \
~~~for~ all ~xin A ~and ~yin B~ where~ cin [0, 1),~~~ ag{I}
end{align}
to cyclic quasi-contraction maps and proved an existence result of best proximity point theorem. The author also posed the question that does this theorem remains true for cyclic quasi-contraction maps?
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%In 2016, Due to the author s errors in proving results, Dung and Radenovic without proving or rejecting theorem of Amini-Harandi, introduced a modified version of it.
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In 2017, Dung and Hang gave negative answer to question of Amini-Harandi and decided to prove his theorem. But they had mistakes in proving theorem.
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In this paper, first we show that the condition eqref{I0} is so strong that theorem of Amini-Harandi (and so modified version of it) is correct by using it alone.
کليدواژه ها
best proximity point; fixed point; cyclic and noncyclic contraction maps; uniformly convex Banach space
نحوه استناد به مقاله
در صورتی که می خواهید در اثر پژوهشی خود به این مقاله ارجاع دهید، به سادگی می توانید از عبارت زیر در بخش منابع و مراجع استفاده نمایید:
اکرم صفری هفشجانی , 1398 , On cyclic strongly quasi-contraction maps , ششمين سمينار آناليز تابعي و كاربردهاي آن