• Title, Summary, Keyword: compatible

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Some Common Fixed Point Theorems using Compatible Maps in Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.2
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    • pp.108-112
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    • 2011
  • Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

Some Common Fixed Points for Type(β) Compatible Maps in an Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.2
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    • pp.147-153
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    • 2013
  • Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

ON COMPATIBLE MAPPINGS OF TYPE (I) AND (II) IN INTUITIONISTIC FUZZY METRIC SPACES

  • Alaca, Cihangir;Altun, Ishak;Turkoglu, Duran
    • Communications of the Korean Mathematical Society
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    • v.23 no.3
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    • pp.427-446
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    • 2008
  • In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

Ultrastructure of Compatible and Incompatible Interactions of Pumpkin Stems Infected with Phytophthora capsici

  • Lee, Byung-Kook;Hong, Jeum-Kyu;Hwang, Byung-Kook
    • The Plant Pathology Journal
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    • v.17 no.1
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    • pp.29-35
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    • 2001
  • Early infection process of Phytophthora capsici in pumpkin stems was similar in the compatible and incompatible interactions 24 h after inoculation. Intercellularly growing hyphae penetrated host parenchyma cells by growing hyphae penetrated host parenchyma cells by forming haustoria. An extrahaustorial matrix was found around the haustoria in both compatible and incompatible interactions. No wall appositions were observed at the infection sites in the parenchyma cells. In the compatible interaction, infecting hyphae grew well in the intercellular spaces between xylem vessels in stem tissues. Degraded host cell wall, plasmolysis of plasma membrane, and degenerated chloroplasts were pathological features of pumpkin stem tissues in both compatible and incompatible interactions. A characteristic host response in the resistant pumkin cultivar Danmatmaetdol was rapid cytoplasmic movement of host cells toward the oomycete haustoria.

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COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN MENGER SPACES

  • Sharma, S.;Choubey, K.
    • The Pure and Applied Mathematics
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    • v.10 no.4
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    • pp.245-254
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    • 2003
  • In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

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COMMON FIXED POINT THEOREMS FOR MAPPINGS ON CONE METRIC SPACES

  • Kim, Jeong-Jin;Bae, Jong-Sook;Cho, Seong-Hoon
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.1067-1075
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    • 2012
  • In this paper we generalize the results of Ili$\acute{c}$ and Rako$\check{c}$evi$\acute{c}$. Also, we generalize one of Berinde's results to cone metric spaces. And we introduce the notion of compatible mappings of type (BC), and we establish a common fixed point theorem for these mappings.