CANTOR'S THEOREM IN 2-METRIC SPACES AND ITS APPLICATIONS TO FIXED POINT PROBLEMS

被引：15

作者：

Lahiri, B. K.

Das, Pratulananda ^{[1
]}

Dey, Lakshmi Kanta ^{[2
]}

机构：

[1] Jadavpur Univ, Dept Math, Kolkata 700032, India

[2] Natl Inst Technol, Dept Math, Durgapur 713209, W Bengal, India

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2011年 / 15卷 / 01期

关键词：

2-Metric spaces; Open ball; Boundedness; Closure; Cantor's Theorem; Baire's Theorem; Contractive mapping; Fixed point;

D O I：

10.11650/twjm/1500406178

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

2-metric space is an interesting nonlinear generalization of metric space which was conceived and studied in details by Gahler. In this paper, for the first time, we establish Cantor's intersection theorem and Baire category theorem in 2-metric spaces. As a departure from normal practice we then apply Cantor's theorem to establish some fixed point theorems in such spaces.

引用

页码：337 / 352

页数：16

共 50 条

[31] FIXED POINT THEOREM IN PROBABILISTIC INNER PRODUCT SPACES AND ITS APPLICATIONS
Huang, Xiao-Qin
Zhu, Chuan-Xi
Liu, Xiao-Jie
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2005, 19 (1-2) : 363 - 370
[32] Extension of Caristi's fixed point theorem to vector valued metric spaces
Agarwal, R. P.
Khamsi, M. A.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (01) : 141 - 145
[33] Fixed point theory in partial metric spaces via φ-fixed point's concept in metric spaces
Jleli, Mohamed
Samet, Bessem
Vetro, Calogero
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[34] Integral Equation via Fixed Point Theorems on a New Type of Convex Contraction in b-Metric and 2-Metric Spaces
Nallaselli, Gunasekaran
Gnanaprakasam, Arul Joseph
Mani, Gunaseelan
Mitrovic, Zoran D.
Aloqaily, Ahmad
Mlaiki, Nabil
MATHEMATICS, 2023, 11 (02)
[35] Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces
Mohamed Jleli
Bessem Samet
Calogero Vetro
Journal of Inequalities and Applications, 2014
[36] Remarks on a common Fixed Point Theorem in compact metric spaces
Imdad, Mohammad
Ali, Javid
MATHEMATICAL COMMUNICATIONS, 2010, 15 (01) : 107 - 116
[37] BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES
Olia, Zeinab Eivazi Damirchi Darsi
Gordji, Madjid Eshaghi
Bagha, Davood Ebrahimi
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2020, 35 (05): : 1239 - 1250
[38] A fixed point theorem on soft G-metric spaces
Guler, Aysegul Caksu
Yildirim, Esra Dalan
Ozbakir, Oya Bedre
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (03): : 885 - 894
[39] A fixed point theorem in generalized ordered metric spaces with application
Gholizadeh, Leila
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2013, 6 (04): : 244 - 251
[40] BASIC PROBLEMS OF THE METRIC FIXED POINT THEORY AND THE RELEVANCE OF A METRIC FIXED POINT THEOREM FOR A MULTIVALUED OPERATOR
Petrusel, A.
Rus, I. A.
Serban, M. A.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2014, 15 (03) : 493 - 513

← 1 2 3 4 5 →