Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Hemant Nashine
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Partial Metric ◽  
New Class ◽  
Weakly Contractive Condition ◽  
Partial Metric Spaces ◽  
Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

scholarly journals Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

2021 ◽  
Vol 37 (2) ◽  
pp. 345-354
Author(s):  
ALEXANDRU-DARIUS FILIP
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

scholarly journals Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5497-5509 ◽  
Author(s):  
Habes Alsamir ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Kamal Abodyah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Partial Metric ◽  
Partially Ordered ◽  
Partial Metric Spaces ◽  
Contraction Type

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

scholarly journals On fixed point theory in partial metric spaces

2012 ◽  
Vol 2012 (1) ◽  
pp. 175 ◽  
Author(s):  
Maryam A Alghamdi ◽  
Naseer Shahzad ◽  
Oscar Valero
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Partial Metric Spaces

Fixed point problems concerning contractive type operators on KST-Spaces

2018 ◽  
Vol 34 (3) ◽  
pp. 287-294
Author(s):  
ARSLAN H. ANSARI ◽  
◽  
LILIANA GURAN ◽  
ABDUL LATIF ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problems ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Contractive Type

In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37–53].

scholarly journals A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3875-3884 ◽  
Author(s):  
Hamid Baghani ◽  
Maryam Ramezani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Set Valued Mappings

In this paper, firstly, we introduce the notion of R-complete metric spaces. This notion let us to consider fixed point theorem in R-complete instead of complete metric spaces. Secondly, as motivated by the recent work of Amini-Harandi (Fixed Point Theory Appl. 2012, 2012:215), we explain a new generalized contractive condition for set-valued mappings and prove a fixed point theorem in R-complete metric spaces which extends some well-known results in the literature. Finally, some examples are given to support our main theorem and also we find the existence of solution for a first-order ordinary differential equation.

scholarly journals Generalized distances and their associate metrics. Impact on fixed point theory

2013 ◽  
Vol 22 (1) ◽  
pp. 23-32
Author(s):  
VASILE BERINDE ◽  
◽  
MITROFAN CHOBAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Cone Metric Spaces ◽  
Generalized Metric Spaces ◽  
Partial Metric Spaces ◽  
Cone Metric

In the last years there is an abundance of fixed point theorems in literature, most of them established in various generalized metric spaces. Amongst the generalized spaces considered in those papers, we may find: cone metric spaces, quasimetric spaces (or b-metric spaces), partial metric spaces, G-metric spaces etc. In some recent papers [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799-1803], [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454], [Samet, B., Vetro, C. and Vetro, F., Remarks on G-Metric Spaces, Int. J. Anal., Volume 2013, Article ID 917158, 6 pages http://dx.doi.org/10.1155/2013/917158], the authors pointed out that some of the fixed point theorems transposed from metric spaces to cone metric spaces, partial metric spaces or G-metric spaces, respectively, are sometimes not real generalizations. The main aim of the present note is to inspect what happens in this respect with b-metric spaces.

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