scholarly journals Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces

2021 ◽  
Vol 37 (2) ◽  
pp. 173-184
Author(s):  
VASILE BERINDE ◽  
MĂDĂLINA PĂCURAR
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Metric Spaces

The main aim of this paper is to establish some fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces, respectively.

scholarly journals Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph

2016 ◽  
Vol 32 (3) ◽  
pp. 293-302
Author(s):  
LASZLO BALOG ◽  
◽  
VASILE BERINDE ◽  
◽  
Keyword(s):  
Banach Space ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Partial Order ◽  
Banach Spaces ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Metric Spaces

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T : K → X that satisfy Rothe’s boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces.

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 On Some Fixed Point Results forH+-Type Contraction Mappings in Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hemant Kumar Pathak ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Contractive Mappings ◽  
Type Contraction

We prove some fixed point theorems forH+-type multivalued contractive mappings in the setting of Banach spaces and metric spaces. The results provided allow recovering different well-known results.

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 Some common fixed point theorems for Ciric type contraction mappings

2012 ◽  
Vol 43 (2) ◽  
pp. 187-202
Author(s):  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Type Contraction

Some common fixed point theorems for \'{C}iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

scholarly journals Note on Common Fixed Point Theorems in Convex Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 28
Author(s):  
Anil Kumar ◽  
Aysegul Tas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Metric Space ◽  
Correct Version ◽  
Convex Metric Spaces ◽  
Set Up ◽  
Common Fixed Point Theorems

In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

scholarly journals Fixed point theorems of finite family with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 155-166
Author(s):  
Singh Saluja
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Convex Metric Spaces

In this paper, we prove that a multi-step iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converges strongly to a common fixed point of the mappings in convex metric spaces. Our results extend and improve the recent result of Kim et al. [9, 10] and many known results.

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