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Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space


Abstract

In this present paper, we establish Cantor's intersection like theorem in a locally convex topological vector spaces. Some fixed point and common fixed point theorems are proved for Reich and Caccioppoli type contractive mappings in such a locally convex topological vector space. Also in this setting we prove a fixed point theorem for some mapping which is the uniform limit of a sequence of Reich type contractive mappings therein.

Встановлена теорема, подібна теоремі Кантора про перетин, у випадку локально опуклих векторних просторів. Для стискуючих відображень типу Райха і Каччіополі відповідних просторів доведені теореми про нерухому точку та спільну нерухому точку. Також у цій постановці доведена теорема про нерухому точку для відображення, яке є рівномірною границею послідовності стискуючих відображень типу Райха.

Key words: Locally convex topological vector space, Cantor's intersection theorem, fixed point.


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Article Information

TitleCantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 262-271
DOI10.31392/MFAT-npu26_3.2020.07
MilestonesReceived 14/06/2020; Revised 02/07/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

A. P. Baisnab
PG Section, Department of Mathematics, Lady Brabourne College, P1/2 Suhrawardy Avenue, Kolkata700017, West Bengal, India.

K. Roy
Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India

M. Saha
Department of Mathematics, The University of Burdwan, Purba Bardhaman-713104, West Bengal, India


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Citation Example

A. P. Baisnab, K. Roy, and M. Saha, Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space, Methods Funct. Anal. Topology 26 (2020), no. 3, 262-271.


BibTex

@article {MFAT1398,
    AUTHOR = {A. P. Baisnab and K. Roy and M. Saha},
     TITLE = {Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {262-271},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2020.07},
       URL = {http://mfat.imath.kiev.ua/article/?id=1398},
}


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