scholarly journals Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Poom Kumam ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Partial Metric ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

scholarly journals On some fixed point theorems for multivalued F-contractions in partial metric spaces

2021 ◽  
Vol 54 (1) ◽  
pp. 151-161
Author(s):  
Santosh Kumar ◽  
Sholastica Luambano
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces

Abstract Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.

scholarly journals Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdullah Shoaib ◽  
Muhammad Arshad ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Monotone Mapping ◽  
Partial Metric Space ◽  
Closed Ball ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results.

scholarly journals Fixed Points forψ-Graphic Contractions with Application to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Hussain ◽  
S. Al-Mezel ◽  
P. Salimi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces

The aim of this paper is to define modified weakα-ψ-contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangularα-admissibility. As an application, we prove new fixed point results for graphic weakψ-contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.

scholarly journals On New χ -Fixed Point Results for λ − Υ , χ -Contractions in Complete Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Babak Mohammadi ◽  
Wutiphol Sintunavarat ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Partial Metric ◽  
Nonlinear Integral Equations ◽  
Complete Metric Spaces ◽  
Partial Metric Spaces ◽  
Theoretical Results

The main aim of this work is to introduce the new concept of λ − Υ , χ -contraction self-mappings and prove the existence of χ -fixed points for such mappings in metric spaces. Our results generalize and improve some results in existing literature. Moreover, some fixed point results in partial metric spaces can be derived from our χ -fixed points results. Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

scholarly journals FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

2020 ◽  
pp. 283
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

scholarly journals Fixed Point Theorems for Geraghty Type Contractive Mappings and Coupled Fixed Point Results in 0-Complete Ordered Partial Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Esra Yolacan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces ◽  
Banach Contraction

We establish new fixed point theorems in 0-complete ordered partial metric spaces. Also, we give remark on coupled generalized Banach contraction. Some examples illustrate the usability of our results. The theorems presented in this paper are generalizations and improvements of the several well known results in the literature.

scholarly journals On contractive mappings and discontinuity at fixed points

2020 ◽  
Vol 14 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Hiranmoy Garai ◽  
Lakshmi Dey ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces ◽  
Contractive Mappings ◽  
Interesting Open Problem

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

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