SOME FIXED POINT RESULTS IN d-COMPLETE TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9837-9847
Author(s):  
S. Rathee ◽  
P. Gupta ◽  
V. Narayan Mishra
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Lower Semi

This paper aims to use T-orbitally lower semi-continuous and $w$-continuous functions in $d$-complete topological spaces to validate some fixed point theorems and extend various known results. The paper also seeks to establish, in the setting of $d$-complete topological spaces, Mizoguchi-Takahashi's type coincidence point theorem for single valued map. The results are supported by illustrative examples.

scholarly journals The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Generalized Contraction ◽  
Common Fixed Point Theorems

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

SOME COMMON FIXED POINT THEOR MS FOR EXPANSIVE MAPPINGS IN d-COMPLETE TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9849-9859
Author(s):  
S. Rathee ◽  
P. Gupta ◽  
V. Narayan Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Topological Spaces ◽  
Expansive Mapping ◽  
Common Fixed Point Theorems

In the present paper, we entrenched common fixed point theorems for self mappings satisfying expansive condition in d-complete topological spaces. Also we prove a fixed point theorem for $(\zeta,\alpha)$-expansive mapping in the setting of d-complete topological spaces. Our results extend and generalize the results of Shahi et al. to d-complete topological spaces.

scholarly journals Fixed point theorems ford-complete topological spaces I

1992 ◽  
Vol 15 (3) ◽  
pp. 435-439 ◽  
Author(s):  
Troy L. Hicks
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Large Class ◽  
Point Theorem ◽  
Distance Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Spaces ◽  
Triangular Inequality ◽  
Banach’S Fixed Point Theorem

Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These included-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.

Fixed Point Theorems for Compatible Mappings of Type (R) in 2-Metric Spaces

2015 ◽  
Vol 2 ◽  
pp. 17-27
Author(s):  
Oinam Budhichandra Singh ◽  
Th. Indubala ◽  
N. Leenthoi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Compatible Mappings

The aim of this paper is to introduce the concept of compatible mappings of type (R) in 2-metric spaces and to prove a coincidence point theorem and a fixed point theorem for compatible mappings of type (R) in 2-matric spaces.

scholarly journals New Fixed Point Results in F-Quasi-Metric Spaces and an Application

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Ehsan Lotfali Ghasab ◽  
Hamid Majani ◽  
Erdal Karapinar ◽  
Ghasem Soleimani Rad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Volterra Type ◽  
Type Integral ◽  
The Given

The main goal of the present paper is to obtain several fixed point theorems in the framework of F-quasi-metric spaces, which is an extension of F-metric spaces. Also, a Hausdorff δ-distance in these spaces is introduced, and a coincidence point theorem regarding this distance is proved. We also present some examples for the validity of the given results and consider an application to the Volterra-type integral equation.

Some Fixed Point Results in Partial Metric Spaces Under Contractive Type Mappings

2020 ◽  
Vol 87 (3-4) ◽  
pp. 219
Author(s):  
G. S. Saluja
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Contractive Type

In this paper, we establish some fixed point theorems and a coincidence point theorem for contractive type mappings in the framework of complete partial metric spaces and give some examples in support of our results. The results presented in this paper extend and generalize several results from the existing literature.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

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