scholarly journals Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Mujahid Abbas ◽  
Basit Ali ◽  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contractive Mapping ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Fixed Point Result ◽  
Invariant Approximation ◽  
New Type

Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalizedF-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

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 Contractibility of Fixed Point Sets of Mean-Type Mappings

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
S. Iampiboonvatana ◽  
P. Chaoha
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Point Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Convex Setting ◽  
Fixed Point Sets

We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.

scholarly journals Coincidence and fixed points for compatible and relatively nonexpansive maps

1993 ◽  
Vol 16 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Gerald Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Nonexpansive Maps ◽  
Relatively Nonexpansive ◽  
Compact Subsets

The concept of relatively nonexpansive maps is introduced. Fixed point and coincidence results for families of four self maps of metric spaces are obtained. Non-continuous compatible and relatively nonexpansive maps on star-shaped compact subsets of normed linear spaces are highlighted, and two theorems of Dotson are generalized.

scholarly journals On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Mi Zhou ◽  
Xiao-Lan Liu ◽  
Adrian Secelean
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Common Property ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
Contraction Condition ◽  
New Type ◽  
The One

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

scholarly journals A new type fixed point theorem for a contraction on partially ordered generalized complete metric spaces with applications

2014 ◽  
Vol 2014 (1) ◽  
pp. 15 ◽  
Author(s):  
Madjid Eshaghi Gordji ◽  
Maryam Ramezani ◽  
Farhad Sajadian ◽  
Yeol Cho ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
New Type

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

scholarly journals On Fixed Points of Asymptotically Regular Mappings

1987 ◽  
Vol 43 (3) ◽  
pp. 328-346 ◽  
Author(s):  
B. E. Rhoades ◽  
S. sessa ◽  
M. S. Khan ◽  
M. Swaleh
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Linear Spaces ◽  
Complete Metric Spaces ◽  
Normed Linear Spaces ◽  
Asymptotically Regular

Some results on fixed points of asymptotically regular mappings are obtained in complete metric spaces and normed linear spaces.The structure of the set of common fixed points is also discussed in Banach spaces. Our work generalizes essentially known results of Das and Naik, Fisher, Jaggi, Jungck, Rhoades, Singh and Tiwari and several others.

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