scholarly journals Some Fixed Point Results on Relational Quasi Partial Metric Spaces and Application to Non-Linear Matrix Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 993
Author(s):  
Reena Jain ◽  
Hemant Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Linear Matrix ◽  
Contractive Condition ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Non Linear

We introduce a qϱ-implicit contractive condition by an implicit relation on relational quasi partial metric spaces and establish new (unique) fixed point results and periodic point results based on it. We justify the results by two suitable examples and compare with them related work. We discuss sufficient conditions ensuring the existence of a unique positive definite solution of the non-linear matrix equation U=B+∑i=1mAi*G(U)Ai, where B is an n×n Hermitian positive definite matrix, A1, A2, ..., Am are n×n matrices, and G is a non-linear self-mapping of the set of all Hermitian matrices which is continuous in the trace norm. Two examples (with randomly generated matrices and complex matrices, respectively) are given, together with convergence and error analysis, as well as average CPU time analysis and visualization of solution in surface plot.

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 Common Fixed Point Results for Four Mappings on Partial Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
A. Duran Turkoglu ◽  
Vildan Ozturk
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Contractive Condition ◽  
Partial Metric ◽  
Partial Metric Spaces

We give fixed point results for four mappings which satisfy almost generalized contractive condition on partial metric space and we support the results with an example.

scholarly journals A common fixed point result by altering distances involving a contractive condition of integral type in partial metric spaces

2013 ◽  
Vol 46 (2) ◽  
Author(s):  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Partial Metric ◽  
Integral Type ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorem

AbstractIn this paper, we present a common fixed point theorem by altering distances for a contractive condition of integral type in partial metric spaces.

On the topology of partial metric spaces

2020 ◽  
Vol 70 (1) ◽  
pp. 135-146
Author(s):  
Dariusz Bugajewski ◽  
Ruidong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Banach Contraction Principle ◽  
Partial Metric ◽  
Ultrametric Spaces ◽  
Partial Metric Spaces ◽  
Banach Contraction ◽  
Necessary And Sufficient

AbstractIn this paper, we give some necessary and sufficient conditions under which the topology generated by a partial metric is equivalent to the topology generated by a suitably defined metric. Next, we study some new extensions of the Generalized Banach Contraction Principle to partial metric spaces. Moreover, we draw a particular attention to the space of all sequences showing, in particular, that some well-known fixed point theorems for ultrametric spaces, can be used for operators acting in that space. We illustrate our considerations by suitable examples and counterexamples.

scholarly journals On a fixed point theorem with application to functional equations

2019 ◽  
Vol 17 (1) ◽  
pp. 1724-1736
Author(s):  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Choonkil Park ◽  
Hasan Mahmood
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Partial Metric ◽  
Ordered Metric Spaces ◽  
Partial Metric Spaces ◽  
Rational Type ◽  
Type Contraction

Abstract The purpose of this paper is to study behavior of a rational type contraction introduced in [A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 2013, 59, 251–258] in context of ordered dualistic partial metric spaces and to investigate sufficient conditions for the existence of a fixed point in this space. These results extend various comparable results, existing in the literature. We give examples to explain our findings. We apply our result to prove the existence of the solution of functional equation.

scholarly journals Boyd and Wong Type Fixed Point Theorems in Partial Metric Spaces

2019 ◽  
Vol 5 (2) ◽  
pp. 251-262
Author(s):  
Faustine Nziku ◽  
Santosh Kumar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Type 3 ◽  
Common Fixed Point Theorem

AbstractIn this paper, we present fixed point results for Boyd and Wong type [3] generalized contractive condition in partial metric spaces. In particular, we generalize the fixed point results due to Akkouchi [1] in complete partial metric spaces in which the continuity requirement for a mapping is relaxed to obtain the results. In addition to that we present a common fixed point theorem for a pair of maps. An illustrative example is also constructed to exhibit the results.

scholarly journals FIXED POINT THEOREMS FOR TWO PAIRS OF MAPPINGS IN PARTIAL METRIC SPACES

2017 ◽  
pp. 969
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Partial Metric ◽  
Compatible Mappings ◽  
Implicit Relation ◽  
Weakly Compatible ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of weakly compatible mappings satisfying a - implicit relation different from the type from [16] is proved. As applications, we obtain the sufficient conditions for the existence of fixed points for a sequence of mappings in partial metric spaces.

Sign in / Sign up

Export Citation Format

Share Document