Comments on "Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric"

被引：4

作者：

Prithvi, B. V. ^{[1
]}

Katiyar, S. K. ^{[2
]}

机构：

[1] SRM Inst Sci & Technol, Dept Math, Chennai 603203, India

[2] Dr BR Ambedkar Natl Inst Technol NIT, Dept Math, Jalandhar 144011, Punjab, India

来源：

TOPOLOGY AND ITS APPLICATIONS | 2024年 / 341卷

关键词：

Contraction; Partial metric space; Fixed point; Picard operator; Iterated function system; Fractal;

D O I：

10.1016/j.topol.2023.108687

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to fill a gap in the article Priya and Uthayakumar (2022) [13]. To prove fractals (fixed points), the authors of that article tried to connect two independent conceptual domains. This results in their main theorem being wrong and becoming a conjecture. This paper scrutinizes and presents both the concepts above to demonstrate fractals in the settings posed in that article. Using a proper definition, the correct theorem to achieve the purpose of that article is discussed. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：11

共 49 条

[41] Generation of fractals via iterated function system of Kannan contractions in controlled metric space
Thangaraj, C.
Easwaramoorthy, D.
Selmi, Bilel
Chamola, Bhagwati Prasad
MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 222 : 188 - 198
[42] Fixed point theorems for generalized weak contractions satisfying rational expression on a ordered partial metric space
Karapınar E.
Marudai M.
Pragadeeswarar V.
Lobachevskii Journal of Mathematics, 2013, 34 (1) : 116 - 123
[43] ON SOME COMMON FIXED POINT THEOREMS FOR GENERALIZED INTEGRAL TYPE F-CONTRACTIONS IN PARTIAL METRIC SPACES
Saluja, Gurucharan Singh
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2022, 37 (04): : 667 - 682
[44] COMMON FIXED POINT THEOREMS FOR MULTI-VALUED CONTRACTIONS SATISFYING GENERALIZED CONDITION(B) ON PARTIAL METRIC SPACES
Beloul, Said
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2015, 30 (05): : 555 - 566
[45] Positive Solution to a Generalized Lyapunov Equation via a Coupled Fixed Point Theorem in a Metric Space Endowed With a Partial Order
Berzig, Maher
Samet, Bessem
FILOMAT, 2015, 29 (08) : 1831 - 1837
[46] Some Common Fixed Point Theorems in Ordered Partial Metric Spaces via F-Generalized Contractive Type Mappings
Dhawan, Pooja
Kaur, Jatinderdeep
MATHEMATICS, 2019, 7 (02)
[47] Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function
Chenkuan Li
Reza Saadati
Joshua Beaudin
Andrii Hrytsenko
Boundary Value Problems, 2023
[48] Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function
Li, Chenkuan
Saadati, Reza
Beaudin, Joshua
Hrytsenko, Andrii
BOUNDARY VALUE PROBLEMS, 2023, 2023 (01)
[49] Common fixed points for generalized α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-implicit contractions in partial metric spaces: consequences and application
Hassen Aydi
Manel Jellali
Erdal Karapınar
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2015, 109 (2): : 367 - 384

← 1 2 3 4 5 →