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اکرم صفری هفشجانی

‎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 ‎ % ‎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? ‎ ‎% %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. ‎ ‎% 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.‎ ‎% 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.

‎best proximity point; fixed point; cyclic and noncyclic contraction maps; uniformly convex Banach space

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صفری هفشجانی، اکرم، 1398، On cyclic strongly quasi-contraction maps، ششمين سمينار آناليز تابعي و كاربردهاي آن، https://conf.ui.ac.ir/fa/archive_index.php?c=sfa&aid=1506169