• Title/Summary/Keyword: common best proximity point

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SOME RESULTS ON COMMON BEST PROXIMITY POINT AND COMMON FIXED POINT THEOREM IN PROBABILISTIC MENGER SPACE

  • Shayanpour, Hamid
    • Journal of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1037-1056
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    • 2016
  • 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.

SOME RESULTS ON BEST PROXIMITY POINT FOR CYCLIC B-CONTRACTION AND S-WEAKLY CYCLIC B-CONTRACTION MAPPINGS

  • V. Anbukkarasi ;R. Theivaraman;M. Marudai ;P. S. Srinivasan
    • The Pure and Applied Mathematics
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    • v.30 no.4
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    • pp.417-427
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    • 2023
  • The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.