Some fixed points of multivalued maps in multiplicative metric spaces (original) (raw)
Some Unique Fixed Point Theorems in Multiplicative Metric Spaces
\"{O}zavsar and Cevikel(Fixed point of multiplicative contraction mappings on multiplicative metric space.arXiv:1205.5131v1 [math.GN] 23 may 2012)initiated the concept of the multiplicative metric space in such a way that the usual triangular inequality is replaced by "multiplicative triangle inequality [Math Processing Error] for all [Math Processing Error]". In this manuscript, we discussed some unique fixed point theorems in the context of multiplicative metric spaces. The established results carry some well known results from the literature to multiplicative metric space. We note that some fixed point theorems can be deduced in multiplicative metric space by using the established results. Appropriate examples are also given.
Fixed points of multiplicative contraction mappings on multiplicative metric spaces
Journal of Engineering and Technology, 2017
In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real numbers R_+ is a complete multiplicative metric space with respect to the multiplicative absolute value function. Furthermore, we introduced concept of multiplicative contraction mapping and proved some fixed point theorems of such mappings on complete multiplicative metric spaces.
Remarks on Multiplicative Metric Spaces and Related Fixed Points
arXiv: General Topology, 2015
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.
Some related fixed point theorems for multivalued mappings on two metric spaces
Carpathian Mathematical Publications, 2020
The definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via FFF-contraction type conditions.
Journal of Inequalities and Applications, 2014
The purpose of this work is to introduce new types of contraction mappings in the sense of a multiplicative metric space. Fixed point results for these contraction mappings in multiplicative metric spaces are obtained. Our presented results generalize, extend, and improve results on the topic in the literature. Moreover, our results cannot be directly obtained as a consequence from the corresponding results in metric spaces. We also state some illustrative examples to claim that our results properly generalize some results in the literature. We apply our main results for proving a fixed point theorem involving a cyclic mapping. MSC: 47H09; 47H10
Common fixed point results for compatible-type mappings in multiplicative metric spaces
Journal of Nonlinear Sciences and Applications, 2016
In this paper, we prove some common fixed point theorems for generalized contractive mappings satisfying some conditions, that is, compatible and compatible-type mappings in multiplicative metric spaces. Our results improve and generalize the corresponding results given in the literature. Moreover, we give some examples to illustrate our main results.
Fixed points of multivalued mappings in metric spaces
2019
Admissibility of mappings are introduced to create conditions to minimally restrict various contractive conditions on pairs of points from a metric space in order to ensure fixed point property of the respective contractions. In the present work we define new admissibility conditions and control functions to obtain certain multivalued fixed point theorems. The corresponding single valued case is discussed. We define four weak contraction mappings of which two are multivalued and two are single valued. The results are without any assumption of continuity. There is an illustrative example.
2011
In this paper we give a common fixed point type generalization for some multi-valued contractive mappings on complete metric spaces. Our results extend some recent results of Y. Feng, S. Liu[ Y. Feng and S. Liu, Fixed point theorem of multi-valued contractive mappings, J. Fixed point theorems for set valued contractions in complete metric spaces, J. Math. Anal. Appl. 334(2007)132-139]. We show that some common fixed point contraction theorems for multi-valued mappings are straightforward consequence of our results.
Some fixed point results for multivalued operators in generalized metric spaces
Computers & mathematics with applications, 2011
Recently, Bucur, Guran and Petrusel presented some results on fixed points of multivalued operators on generalized metric spaces which extended some old fixed point theorems to the multivalued case (Bucur et al., 2009 [7]). Also, Kikkawa and Suzuki have proved some results for generalized contractions in complete metric spaces (Kikkawa, 2008 [9]). In this paper, we shall give some results on fixed points of multivalued operators on generalized metric spaces by using the method of Kikkawa (2008) [9].
Fixed point results in multiplicative generalized metric spaces
Advances in Fixed Point Theory, 2016
In this paper, first we introduce the notion of multiplicative generalized metric spaces and then prove the Banach contraction principle in setting of newly defined spaces. We also introduce the notion of weakly commuting, compatible maps and its variants, weakly compatible, weakly compatible with properties (E.A) and CLR in this space. Further, we prove some fixed point theorems on multiplicative generalized metric spaces and provide some suitable examples in support of our results.
Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application
International Journal of Mathematics and Mathematical Sciences, 2015
The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.
A Suzuki fixed point theorem for generalized multivalued mappings on metric-like spaces
Glasnik Matematicki
Based on a new papers of Aydi et al. in [7, 8], where the concept of Hausdorff metric-like has been initiated, we introduce Suzuki type contractive multivalued mappings on metric-like spaces. We also establish several fixed point results involving such contractions. We show that many known fixed point results in literature are simple consequences of our theorems. Our obtained results are supported by some examples and an application.
Fixed Point Results for Multivalued Mapping in R-Metric Space
This paper explores certain fixed point results for multivalued mapping in a metric space endowed with an arbitrary binary relation R, briefly written as R-metric space. The fixed point results proved are subjected to contraction conditions corresponding to the multivalued counterpart of F-contraction and F-weak contraction in R-metric space. The main results unify, extend and generalize the results on multivalued and single-valued mapping in the literature. To support the conclusion, several examples have been provided.
Fixed Points of Multivalued Maps Via-Contraction
2016
In this paper, we extend the notion of) , ( G-contraction, introduced by Ozturk and Girgin, to multi-valued mappings. By using our new notion we prove a fixed point theorem for multi-valued mappings. Our results imply Nadler's theorem, and generalized version of Nadler's theorem on partial metric spaces.
Common Fixed Point Theorem in a Multiplicative S -Metric Space With an Application
Communications in Mathematics and Applications, 2021
In this paper, we introduce multiplicative \(S\)-metric space as a generalization of multiplicative \(d\)-metric space and investigate its some topological properties. Further, we establish a common fixed point theorem for a pair of self maps in the framework of multiplicative \(S\)-metric space with an application. This result generalizes some fixed point results in the current literature. Finally, we provide an example in support of the result.
Common fixed point theorems for multivalued mappings
Pacific Journal of Mathematics, 1981
Some results on common fixed points for a pair of multivalued mappings defined on a closed subset of a complete metric space are obtained. Our work extends some of the known results due to Itoh; Isέki; and Rus.