scholarly journals Fixed point theorems for metric spaces with a conical geodesic bicombing

2017 ◽  
Vol 38 (5) ◽  
pp. 1642-1657 ◽  
Author(s):  
GIULIANO BASSO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Existence Result ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probability Measures

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a $1$-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.

scholarly journals Fixed points of multivalued nonexpansive maps

1991 ◽  
Vol 14 (3) ◽  
pp. 421-430 ◽  
Author(s):  
T. Husain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Nonexpansive Maps ◽  
Contractive Type ◽  
Bounded Convex ◽  
Convex Subsets

Fixed point theorems for multivalued contractive-type and nonexpansive-type maps on complete metric spaces and on certain closed bounded convex subsets of Banach spaces have been proved. They extend some known results due to Browder, Husain and Tarafdar, Karlovitz and Kirk.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

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.

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

scholarly journals Some fixed point theorems on equivalent metric spaces

2021 ◽  
Vol 38 (1) ◽  
pp. 139-148
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
MARIANA CUFOIAN ◽  
ADRIANA MITRE
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Complete Metric Spaces

This paper aims to analyze the existence of fixed points for mappings defined on complete metric spaces satisfying almost contractive conditions and a general contractive inequality of integral type. The existence of a fixed point is ensured by hypotheses formulated in terms of equivalent metric spaces.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

scholarly journals Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations

2000 ◽  
Vol 158 ◽  
pp. 73-86
Author(s):  
Jinqing Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Maximal And Minimal Solutions

AbstractIn this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.

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