• Title/Summary/Keyword: common fied point

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COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS WITH ψ-ϕ-CONTRACTIVE OR EXPANSIVE TYPE CONDITIONS ON COMPLEX-VALUED METRIC SPACES

  • JIN, HAI-LAN;PIAO, YONG-JIE
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.451-463
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    • 2015
  • A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.