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Shayanpour, Hamid Korean Mathematical Society 2016 대한수학회지 Vol.53 No.5
In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.
Hamid Shayanpour 대한수학회 2016 대한수학회지 Vol.53 No.5
In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized $\varphi$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized $\varphi$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.