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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.
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참고문헌 (27)
참고문헌 신청
M. A. Al-Thagafi / 2009 / Convergence and existence results for best proximity points / Nonlinear Anal 70(10):3665~3671
A. Amini-Harandi / 2013 / Best proximity points for proximal generalized contractions in metric spaces / Optim. Lett 7(5):913~921
A. Amini / 2013 / Best proximity point theorems for cyclic strongly quasi-contraction mappings / J. Global Optim 56(4):1667~1674
A. Amini / 2014 / Common best proximity points theorems in metric spaces / Optim. Lett 8(2):581~589
J. Anuradha / 2009 / Proximal pointwise contraction / Topology Appl 156(18):2942~2948
A. Amini-Harandi / 2013 / Best proximity points for proximal generalized contractions in metric spaces / Optim. Lett 7(5):913~921
A. Amini / 2013 / Best proximity point theorems for cyclic strongly quasi-contraction mappings / J. Global Optim 56(4):1667~1674
A. Amini / 2014 / Common best proximity points theorems in metric spaces / Optim. Lett 8(2):581~589
J. Anuradha / 2009 / Proximal pointwise contraction / Topology Appl 156(18):2942~2948
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