Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
New Applications of γ-Quasiconvexity Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory

verfasst von : Nihal Yılmaz Özgür, Nihal Taş

Erschienen in: Applications of Nonlinear Analysis

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper is a research survey about the fixed-point (resp. fixed-circle) theory on metric and some generalized metric spaces. We obtain new generalizations of the well-known Rhoades’ contractive conditions, Ćiri ć’s fixed-point result and Nemytskii-Edelstein fixed-point theorem using the theory of an S b-metric space. We present some fixed-circle theorems on an S b -metric space as a generalization of the known fixed-circle (fixed-point) results on a metric and an S-metric space.
The content of this section is divided into the following:
1.
Introduction
 
2.
Some Generalized Metric Spaces
 
3.
New Generalizations of Rhoades’ Contractive Conditions
 
4.
Some Generalizations of Nemytskii-Edelstein and Ćirić’s Fixed-Point Theorems
 
5.
Some Fixed-Circle Theorems
 

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel A Multiple Hilbert-Type Integral Inequality in the Whole Space
Nächstes Kapitel Finite-Difference Modeling of Nonlinear Phenomena in Time-Domain Electromagnetics: A Review
Literatur
1.
A. Aghajani, M. Abbas, J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered G b -metric spaces. Filomat 28(6), 1087–1101 (2014)MathSciNetCrossRef
2.
A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces. Numer. Funct. Anal. Optim. 32(3), 243–253 (2011)MathSciNetCrossRef
3.
4.
I.A. Bakhtin, The contraction mapping principle in almost metric space. Funct. Anal., Ulianowsk. Gos. Ped. Ins. 30, 26–37 (1989)
5.
S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals. Fundam. Math. 2, 133–181 (1922)CrossRef
6.
M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces. Cent. Eur. J. Math 8(2), 367–377 (2010)MathSciNetCrossRef
7.
J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241–251 (1976)MathSciNetCrossRef
8.
B. Chaudhary, S. Nanda, Functional Analysis with Applications (Wiley Eastern Limited, New Delhi, 1989)
9.
10.
11.
E.T. Copson, Metric Space (Universal Bookstall, New Delhi, 1996)
12.
B.C. Dhage, Generalized metric spaces mappings with fixed point. Bull. Calcutta Math. Soc. 84, 329–336 (1992)
13.
M. Edelstein, On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, 74–79 (1962)MathSciNetCrossRef
14.
Ö. Ege, Complex valued G b-metric spaces. J. Comput. Anal. Appl. 21(2), 363–368 (2016)
15.
S. G\(\overset {..}{a}\)hler, 2-metrische R\(\overset {..}{a }\)ume und iher topoloische Struktur. Math. Nachr. 26, 115–148 (1963)MathSciNetCrossRef
16.
A. Gupta, Cyclic contraction on S-metric space. Int. J. Anal. Appl. 3(2), 119–130 (2013)
17.
N.T. Hieu, N.T. Ly, N.V. Dung, A generalization of ciric quasi-contractions for maps on S-metric spaces. Thai J. Math. 13(2), 369–380 (2015)
18.
P.K. Jain, A. Khalil, Metric Space (Narosa Publishing House, New Delhi, 1996)
19.
G.A. Jones, D. Singerman, Complex Functions an Algebraic and Geometric Viewpoint (Cambridge University Press, New York, 1987)
20.
A.N. Kolmogorov, S.V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover Publication, New York, 1957)
21.
A.N. Kolmogorov, S.V. Fomin, Introductory Real Analysis (Dover Publication, New York, 1970)
22.
E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1978)
23.
D.P. Mandic, The use of Möbius transformations in neural networks and signal processing, in Proceedings of Neural Networks for Signal Processing X 1 and 2, pp. 185–194 (2000)
24.
J.E. Marsden, Elementary Classica1 Analysis (W. H. Freeman and Company, SanFrancisco, 1974)
25.
N.M. Mlaiki, Common fixed points in complex S -metric space. Adv. Fixed Point Theory 4(4), 509–524 (2014)
26.
Z. Mustafa, B. Sims, A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7, 289–297 (2006)
27.
V.V. Nemytskii, The fixed point method in analysis. Usp. Mat. Nauk 1, 141–174 (1936) [in Russian]
28.
N. Özdemir, B.B. İskender, N.Y. Özgür, Complex valued neural network with Möbius activation function. Commun. Nonlinear Sci. Numer. Simul. 16(12), 4698–4703 (2011)MathSciNetCrossRef
29.
N.Y. Özgür, N. Taş, Some Generalizations of Fixed Point Theorems on S-Metric Spaces. Essays in Mathematics and Its Applications in Honor of Vladimir Arnold (Springer, New York, 2016)
30.
N.Y. Özgür, N. Taş, Some generalizations of the Banach’s contraction principle on a complex valued S -metric space. J. New Theory 2(14), 26–36 (2016)
31.
32.
N.Y. Özgür, N. Taş, Some fixed point theorems on S-metric spaces. Mat. Vesnik 69(1), 39–52 (2017)
33.
34.
N.Y. Özgür, N. Taş, Fixed-circle problem on S-metric spaces with a geometric viewpoint. arXiv:1704.08838 [math.MG]
35.
N.Y. Özgür, N. Taş, Common fixed point results on complex valued S-metric spaces (submitted for publication)
36.
N.Y. Özgür, N. Taş, Some generalized fixed-point theorems on complex valued S-metric spaces (submitted for publication)
37.
N.Y. Özgür, N. Taş, The Picard theorem on S-metric spaces, Acta Math. Sci. (in press)
38.
N.Y. Özgür, N. Taş, Çelik, U.: Some fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9(2), 10–23 (2017)
39.
N.Y. Özgür, N. Taş, A note on “Best proximity point results in S-metric spaces” with some topological aspects (submitted for publication)
40.
B.E. Rhoades, A comparison of various definitions of contractive mappings. Trans. Am. Math. Soc. 226, 257–290 (1977)MathSciNetCrossRef
41.
S. Sedghi, N.V. Dung, Fixed point theorems on S -metric spaces. Mat. Vesnik 66(1), 113–124 (2014)MathSciNetMATH
42.
S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in D∗-metric spaces. Fixed Point Theory Appl. 2007, Article ID 27906, 13 pp. (2007)
43.
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces. Mat. Vesnik 64(3), 258–266 (2012)MathSciNetMATH
44.
S. Sedghi, A. Gholidahneh, T. Došenović, J. Esfahani, S. Radenović, Common fixed point of four maps in S b -metric spaces. J. Linear Topol. Algebra 5(2), 93–104 (2016)MathSciNet
45.
H. Siddique, Functional Analysis with Applications (Tata McGraw-Hill Publishing Company, New Delhi, 1986)
46.
N. Souayah, N. Mlaiki, A fixed point theorem in S b-metric spaces. J. Math. Comput. Sci. 16, 131–139 (2016)CrossRef
47.
48.
N. Taş, N.Y. Özgür, New generalized fixed point results on S b-metric spaces. arXiv:1703.01868 [math.GN]
49.
M. Ughade, D. Turkoglu, S.R. Singh, R.D. Daheriya, Some fixed point theorems in A b-metric space. Br. J. Math. Comput. Sci. 19(6), 1–24 (2016)CrossRef
50.
Wolfram Research, Inc., Mathematica, Trial Version, Champaign, IL (2016)
Metadaten
Titel
Generalizations of Metric Spaces: From the Fixed-Point Theory to the Fixed-Circle Theory
verfasst von
Nihal Yılmaz Özgür
Nihal Taş
Copyright-Jahr
2018
Buch
Applications of Nonlinear Analysis

Print ISBN: 978-3-319-89814-8

Electronic ISBN: 978-3-319-89815-5

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-89815-5_28