Fixed point theorems for 1-set weakly contractive and pseudocontractive operators on an unbounded domain

2011 ◽  
pp. 125-147 ◽  
Author(s):  
Afif Ben Amar ◽  
Jesús Garcia-Falset
Keyword(s):  
Fixed Point ◽  
Unbounded Domain ◽  
Fixed Point Theorems ◽  
Weakly Contractive

Fixed point theorems for generalized weakly contractive mappings

2011 ◽  
Vol 74 (6) ◽  
pp. 2116-2126 ◽  
Author(s):  
Binayak S. Choudhury ◽  
P. Konar ◽  
B.E. Rhoades ◽  
N. Metiya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Weakly Contractive

scholarly journals Fixed point theorems in partial metric spaces with an application

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 617-624
Author(s):  
H.P. Masiha ◽  
F. Sabetghadam ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Fractional Boundary Value Problem ◽  
Partial Metric Spaces ◽  
Contractive Type ◽  
Ordered Partial Metric Space ◽  
Weakly Contractive

Matthews [12] introduced a new distance P on a nonempty set X, which he called a partial metric. The purpose of this paper is to present some fixed point results for weakly contractive type mappings in ordered partial metric space. An application to nonlinear fractional boundary value problem is also presented.

scholarly journals Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

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.

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