scholarly journals A converse to Banach's fixed point theorem and its CLS-completeness

2018 ◽  
Author(s):  
Constantinos Daskalakis ◽  
Christos Tzamos ◽  
Manolis Zampetakis
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach’S Fixed Point Theorem

scholarly journals On New Type of F -Contractive Mapping for Quasipartial b -Metric Spaces and Some Results of Fixed-Point Theorem and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
A. M. Zidan ◽  
Asma Al Rwaily
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Banach’S Fixed Point Theorem ◽  
Contractive Type ◽  
New Type

In this paper, we introduce the concept of new type of F -contractive type for quasipartial b-metric spaces and some definitions and lemmas. Also, we will prove a new fixed-point theorem in quasipartial b -metric spaces for F -contractive type mappings. In addition, we give an application which illustrates a situation when Banach’s fixed-point theorem for complete quasipartial b -metric spaces cannot be applied, while the conditions of our theorem are satisfying.

scholarly journals Fixed Point Theorems for Set-Valued Mappings under Contractive Condition in Quasi-Metric Spaces

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Mohseni Kolagar ◽  
Y.J. Cho ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Generalized Weak Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Set Valued Mappings ◽  
Weakly Contractive

Abstract In this paper, we introduce the concept of a generalized weak contraction for set-valued mappings defined on quasi-metric spaces. We show the existence of fixed points for generalized weakly contractive set-valued mappings. Indeed, we have a generalization of Nadler’s fixed point theorem and Banach’s fixed point theorem in quasi-metric spaces and, further, investigate the convergence of iterate scheme of the form xn+1 ∈ Fxn with error estimates.

scholarly journals Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Lijie Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Almost Automorphic ◽  
Banach’S Fixed Point Theorem ◽  
Lipschitz Conditions ◽  
Stochastic Functional

The existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. Finally, an example illustrating our main result is given.

A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space

2018 ◽  
Vol 68 (5) ◽  
pp. 1113-1116 ◽  
Author(s):  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Solution ◽  
Banach Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Rectangular Metric Space

Abstract In this note we give very short proofs for Banach contraction principle theorem in the b-rectangular metric spaces and b-metric spaces. Our result provides a complete solution to an open problem raised by George, Radenović, Reshma and Shukla.

A common generalization of metric, ultrametric and topological fixed point theorems

2015 ◽  
Vol 27 (1) ◽  
Author(s):  
Katarzyna Kuhlmann ◽  
Franz-Viktor Kuhlmann
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Abelian Groups ◽  
Common Generalization ◽  
Banach’S Fixed Point Theorem

AbstractWe present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's fixed point theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not involving any metrics. We demonstrate its applications to the metric, ultrametric and topological cases, and to ordered abelian groups and fields.

scholarly journals Maia type fixed point results via C-class function

2020 ◽  
Vol 12 (2) ◽  
pp. 227-244
Author(s):  
Arslan Hojat Ansari ◽  
Mohammad Saeed Khan ◽  
Vladimir Rakočević
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Binary Relation ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Class Function ◽  
Banach’S Fixed Point Theorem

AbstractIn 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.

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.

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