scholarly journals Some Generalised Fixed Point Theorems Applied to Quantum Operations

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 759
Author(s):  
Umar Batsari Yusuf ◽  
Poom Kumam ◽  
Sikarin Yoo-Kong
Keyword(s):  
Fixed Point ◽  
Quantum State ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Quantum States ◽  
Contractive Condition ◽  
Quantum Operation ◽  
Quantum Operations ◽  
Finite Dimensional

In this paper, we consider an order-preserving mapping T on a complete partial b-metric space satisfying some contractive condition. We were able to show the existence and uniqueness of the fixed point of T. In the application aspect, the fidelity of quantum states was used to establish the existence of a fixed quantum state associated to an order-preserving quantum operation. The method we presented is an alternative in showing the existence of a fixed quantum state associated to quantum operations. Our method does not capitalise on the commutativity of the quantum effects with the fixed quantum state(s) (Luders’s compatibility criteria). The Luders’s compatibility criteria in higher finite dimensional spaces is rather difficult to check for any prospective fixed quantum state. Some part of our results cover the famous contractive fixed point results of Banach, Kannan and Chatterjea.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1212
Author(s):  
Mathuraiveeran Jeyaraman ◽  
Mookiah Suganthi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Periodic and fixed point theorems in a quasi-metric space

1993 ◽  
Vol 54 (1) ◽  
pp. 80-85 ◽  
Author(s):  
Ljubomir Ćirić
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contractive Condition ◽  
Common Fixed Point Theorem

AbstractGeneral periodic and fixed point theorems are proved for a class of self maps of a quasi-metric space which satisfy the contractive definition (A) below. Two examples are presented to show that the class of mappings which satisfy (A) is indeed wider than a class of selfmaps which satisfy Caristi's contractive definition (C) below. Also a common fixed point theorem for a pair of maps which satisfy a contractive condition (D) below is established.

Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

2017 ◽  
Vol 33 (3) ◽  
pp. 301-310
Author(s):  
MELANIA-IULIA DOBRICAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Theorems ◽  
Mixed Monotone Property ◽  
First Order ◽  
System Equation ◽  
Coupled Fixed Points

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

Fixed Point Theorems for Faintly Compatible Mappings in Intuitionistic Fuzzy Metric Space

2017 ◽  
Vol 84 (1-2) ◽  
pp. 130 ◽  
Author(s):  
Kamal Wadhwa ◽  
Ved Prakash Bhardwaj
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Compatible Mappings ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems

In this paper, we correct the contractive condition of Manro and Kang [16] and prove some common fixed point theorems for four faintly compatible mappings using subsequential continuous mappings in Intuitionistic Fuzzy metric spaces. We also provide an example in support of our main result. Our results improve and generalize the results of Manro and Kang [16].

Fixed point results on complete G-metric spaces

2011 ◽  
Vol 48 (3) ◽  
pp. 304-319 ◽  
Author(s):  
Zead Mustafa ◽  
Mona Khandagji ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces

In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, dG). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.

scholarly journals Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Meryam Cherichi ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Fixed Point Theorems ◽  
Second Order ◽  
Uniqueness Of Solution ◽  
Contractive Condition ◽  
Initial Value ◽  
Gauge Space

We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.

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