Existence and stability theorems in vector-valued metric spaces for fixed point and coincidence point problems governed by multi-valued weak contractions
研究了向量值度量空间中满足弱压缩条件的多值算子的不动点存在性与稳定性，并讨论了重合点问题和最佳逼近点问题。
Abstract In this work, in the setting of a vector-valued metric space X , the fixed point inclusion $$x\in G(x), x\in X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>G</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> governed by a multi-valued operator $$G:X\multimap X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>⊸</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> satisfying a weak contraction type condition on its graph is studied. Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.