Covering mappings in metric spaces and fixed points

In this paper, some common fixed point theorems for Lipschitz-type fuzzy mappings in complete metric spaces are obtained. As applications, we establish some common fixed point theorems for Lipschitz-type multi-valued mappings in complete metric spaces. Also, we give an example to show the validity of our results, which indicates that our results improve and extend several known results in the existing literature.MSC:47H10, 47H04, 26A16.

Samet et al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced a new, simple and unified approach by using the concepts of α-ψ-contractive type mappings and α-admissible mappings in metric spaces and presented some nice fixed point results. Recently, Sridevi et.al (International Journal of Mathematics Trends and Technology, Volume 48, Number 3 August 2017) proposed the concept of α-ψ- contraction and generalized α-ψ- for self map in digital metric spaces. The purpose of this paper is to present a new class of contractive pair of mappings called α--ψ- contraction and generalized α--ψ- contractive pair of mappings and study various fixed point theorems for such mappings in digital metric spaces. For this, we introduce a new notion of α--admissible w.r.t T mapping which in turn generalizes the concept of g-monotone mapping recently given by “Ciric et al. (Fixed Point Theory Appl. 2008 (2008), Article ID 131294, 11 pages)”. Also, we give some fixed point theorems for cyclic contractive mapping in such spaces. The presented theorems hold without using completeness of the space and without the assumption of continuity of the given mappings. Our results extend, generalize and subsumes digital version of various known comparable results [[1-4,8,13,16,18-22], worth to mention here]. Some illustrative examples are quoted to demonstrate the main results.

A new, simple and unified approach in the theory of contractive mappings was recently given by Samet \emph{et al.} (Nonlinear Anal. 75, 2012, 2154-2165) by using the concepts of $\alpha$-$\psi$-contractive type mappings and $\alpha$-admissible mappings in metric spaces. The purpose of this paper is to present a new class of contractive pair of mappings called generalized $\alpha$-$\psi$ contractive pair of mappings and study various fixed point theorems for such mappings in complete metric spaces. For this, we introduce a new notion of $\alpha$-admissible w.r.t $g$ mapping which in turn generalizes the concept of $g$-monotone mapping recently introduced by $\acute{C}$iri$\acute{c}$ et al. (Fixed Point Theory Appl. 2008(2008), Article ID 131294, 11 pages). As an application of our main results, we further establish common fixed point theorems for metric spaces endowed with a partial order as well as in respect of cyclic contractive mappings. The presented theorems extend and subsumes various known comparable results from the current literature. Some illustrative examples are provided to demonstrate the main results and to show the genuineness of our results.

In this article, we investigate the relationship between freely quasiconformal mappings and locally weakly quasisymmetric mappings in quasiconvex and complete metric spaces. We first prove the equivalence of freely quasiconformal mappings, ring properties, and locally weakly quasisymmetric mappings. Finally, we prove that the composition of two locally weakly quasisymmetric mappings in metric spaces is locally weakly quasisymmetric mapping.

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for contraction mapping in metric spaces, have developed rapidly in recent years. Some of the things that support the development of generalization are the emergence of mappings that are more general than contraction mappings and the emergence of spaces that are more general than metric spaces. The generalized Kannan type mappings are one of the mappings that are more general than contraction mappings. Furthermore, some of the more general spaces than metric spaces are b-metric spaces and modular b-metric spaces, which bring the concept of b-metric spaces into modular spaces. The fixed-point theorems for generalized Kannan-type mappings on b-metric spaces have been given. Therefore, this research aims to define generalized Kannan-type mappings on modular b-metric spaces and provide fixed point theorems for the generalized Kannan-type mappings on complete modular b-metric spaces. The definition of generalized Kannan type mapping in modular b-metric spaces is given by generalizing generalized Kannan type mappings in b-metric spaces. Then, the proof of fixed-point theorems for that mapping in modular b-metric spaces is carried out analogously to the proof of the fixed-point theorems for that mapping given in b-metric space. In this article, we obtain the definition of Kannan-type mappings and fixed-point theorems for generalized Kannan-type mappings in modular b-metric spaces and some consequences of the fixed-point theorem. In proving the theorem, a property of altering distance functions in b-metric spaces is generalized into modular b-metric spaces.

This paper aims to discuss the update of the comparative study of non-commuting mappings in metric space and probabilistic metric space. This interrelationship study in weaker commuting maps helps researchers understand, analyze, and reach their research goal.

KKM mappings in cone metric spaces and some fixed point theorems

On common fixed point theorems for non-self hybrid mappings in convex metric spaces

New cone fixed point theorems for nonlinear multivalued maps with their applications

Recently Suzuki (2008) and then Kikkawa and Suzuki (2008) gave a new generalization of the Banach contraction principle. Then, Mot and Petrusel (2009), Dhompapangasa and Yingtaweesttikulue (2009), Bose and Roychowd- hury (2011), Singh and Mishra (2010), and Doric and Lazovic (2011) further extended their work. Recently Bose (2012) obtained some Suzuki-type common fixed point theorems for generalized contractive multivalued mappings using a result of Bose and Mukherjee(1977) which extend the previously obtained re- sults. Recently Damjanovic and Doric(2011) obtained a multivalued generaliza- tion of theorems Kikkawa and Suzuki (2008) concerning Kannan mappings. Also Singh and Mishra (2010) considered coincidence and fixed point theorems for a class of hybrid pair of single-valued and multi-valued maps in metric space setting and Singh et al (2012) prsented a common fixed point theorem for a pair of multi-valued maps in a complete metric space extending a recent theorem of Doric and Lazovic. First we generalize the theorem of Singh et al which also extend the theorem of Singh and Mishra(2010). Then we extend the theorem of Damjanovic and Doric to a common fixed point theorem of a pair of mul- tivalued mappings. As an application, we consider the existence of a common solution for a class of functional equations arising in dynamic programming.

We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988). Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.

In the present paper, the concept of nonlinear $F$-contraction formultivalued mappings in metric spaces is introduced and considering the new proof technique, which was used for single valued maps by Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 2012:94, 6 pp.], we demonstrate that multivalued nonlinear $F$-contractions of C iri c type are weakly Picard operators on complete metric spaces. Finally, we give a nontrivial example to guarantee that our result is veritable generalization of recent result of C iri c [Lj. B. C iri c , Multi-valued nonlinear contraction mappings, Nonlinear Analysis , 71 (2009), 2716-2723]. Also, we show that many fixed point results in the literature can not be applied to this example.

In this paper we introduce the concept of generalized weakly contractiveness for a pair of multivalued mappings in a metric space. We then prove the existence of a common fixed point for such mappings in a complete metric space. Our result generalizes the corresponding results for single valued mappings proved by Zhang and Song (14), as well as those proved by D. Doric (4).

This paper aims to introduce several new classes of contraction mappings inspired by convex and rational contraction mappings. We establish the existence and uniqueness of fixed points for each newly proposed contraction mapping in metric spaces. To validate our theoretical findings, we provide several illustrative examples that demonstrate cases where well-known fixed point results, such as the Banach contraction principle, the Kannan fixed point theorem, the Chatterjea fixed point theorem, the Jaggi fixed point theorem, and the Istratescu fixed point theorem, are not applicable. As an application, we employ our theoretical fixed point results to investigate the existence and uniqueness of solutions to nonlinear implicit integral equations.

Fixed point results for generalized quasicontraction mappings in abstract metric spaces