34 papers found.

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Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the ...

In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: u ( s ) = ϕ i ( s ) + ∫ a b K i ( s , r , u ( r ) ) d r , where s ∈ ( a , b ) ⊆ R ; u , ϕ i ∈ C ( ( a , b ) , R n ) and K i : ( a , b ) ...

In this paper we consider, discuss, improve and generalize recent b-(E.A)-property results for mappings in b-metric spaces established by Ozturk and Turkoglu (J Nonlinear Convex Anal 16(10):2059–2066, 2015). Thus, all our results are with much shorter proofs. One example is given to support the result.

Very recently, Ma et al. (Fixed Point Theory Appl. 2014:206, 2014) introduced \(C^{*}\)-algebra-valued metric spaces as a new concept. Also, Ma and Jiang (Fixed Point Theory Appl. 2015:222, 2015), generalizing this concept, introduced \(C^{*}\)-algebra-valued b-metric spaces. In both frameworks, these and other authors proved some fixed point results. We show in this paper that all ...

In this paper, we consider, discuss, improve, and complement recent fixed points results for mappings satisfying cyclical contractive conditions established by Pacurar and Rus (Nonlinear Anal. 72:1181-1187, 2010) and Chandok and Postolache (Fixed Point Theory Appl. 2013:28, 2013). By using a new lemma we get much shorter and nicer proofs of some results with the new concept of ...

The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by He et al. (Fixed Point Theory Appl. 2014:48, 2014), Mongkolkeha and Sintunavarat (J. Nonlinear Sci. Appl. 8:1134-1140, 2015) and ...

We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed ...

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, 2013) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping.

The purpose of this paper is to establish some fixed point results for cyclic contractions in the setting of dislocated quasi-b-metric spaces. We verify that some previous cyclic contraction results in dislocated quasi-b-metric spaces are just equivalent to the non-cyclic ones in the same spaces. Moreover, by using two examples, we highlight the superiority of the results obtained.

In this paper, we first present some elementary results concerning cone metric spaces over Banach algebras. Next, by using these results and the related ones about c-sequence on cone metric spaces we obtain some new fixed point theorems for the generalized Lipschitz mappings on cone metric spaces over Banach algebras without the assumption of normality. As a consequence, our main ...

The aim of this article is to present, improve and generalize some recent coincidence and coupled coincidence point results from several papers in the framework of partially ordered b-metric spaces. Two examples are also provided to support the superiority of the obtained results.

In this paper, by using Minkowski functional introduced by Kadelburg et al. (Appl. Math. Lett. 24:370-374, 2011) or nonlinear scalarization function introduced by Du (Nonlinear Anal. 72:2259-2261, 2010), we prove some equivalences between vectorial versions of fixed point theorems for H-cone metrics in the sense of Arshad and Ahmad and scalar versions of fixed point theorems for ...

In this paper we present some coincidence point results for four mappings satisfying generalized \(( \psi,\varphi ) \)-weakly contractive condition in the framework of ordered b-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of Nashine and Samet (Nonlinear Anal. 74:2201-2209, 2011) and Shatanawi and Samet (Comput. Math. Appl. ...

In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uniqueness of a common coupled fixed point. An example illustrating our results is provided.

In this paper, we proved common coupled fixed point results for mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces. Our results extend and generalize several well-known comparable results in literature.

The purpose of this paper is to discuss the existence of fixed points for new classes of mappings defined on an ordered metric space. The obtained results generalize and improve some fixed point results in the literature. Some examples show the usefulness of our results. MSC:46N40, 47H10, 54H25, 46T99.

Using a combination of techniques introduced by Jleli and Samet (Fixed Point Theory Appl. 2012:210, 2012) and Samet et al. (Int. J. Anal. 2013:917158, 2013) on the one hand, and by Kadelburg et al. (Bull. Math. Anal. Appl. 4:51-63, 2012) on the other hand, we show that several coupled fixed point results in (ordered) G-metric spaces obtained recently are simple consequences of the ...

In this paper, tripled coincidence points of mappings satisfying some nonlinear contractive conditions in the framework of partially ordered b-metric spaces are obtained. Our results extend the results of Berinde and Borcut (Nonlinear Anal. 74:4889-4897, 2011) and Borcut (Appl. Math. Comput. 218:7339-7346, 2012) from the context of ordered metric spaces to the setting of ordered ...

In this paper, we introduce the notion of 0-σ-complete metric-like space and prove some common fixed point theorems in such spaces. Our results unify and generalize several well-known results in the literature and the recent result of Amini-Harandi [Fixed Point Theory Appl. 2012:204, 2012]. Some examples are included which show that the generalization is proper.

In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature.MSC: 47H10, 54H25.