The main aim of this paper is to introduce the concept of N-b-cone metric spaces over a Banach algebra as a generalization of N-cone metric spaces over a Banach algebra and b-metric spaces. Also, we study some coupled...
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The main aim of this paper is to introduce the concept of N-b-cone metric spaces over a Banach algebra as a generalization of N-cone metric spaces over a Banach algebra and b-metric spaces. Also, we study some coupled common fixed point theorems for generalized Lipschitz mappings in this framework. Finally, we give an example and an application to the existence of solutions of integral equations to illustrate the effectiveness of our generalizations. Some results in the literature are special cases of our results.
This note is intended as an attempt at presenting some topological properties in cone metric spaces over Banach algebras. Moreover, the corresponding fixed point results are given. In addition, the P property, T-stabi...
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This note is intended as an attempt at presenting some topological properties in cone metric spaces over Banach algebras. Moreover, the corresponding fixed point results are given. In addition, the P property, T-stability of Picard's iteration, well-posedness of fixed point problems are also displayed. Our results complement and generalize some previous results in the existing literature.
In this paper, we introduce the concept of hexagonal cone b-metric spaces over Banach algebras as a generalization of cone hexagonal metric spaces and cone b-hexagonal metric spaces. An example is given at the end of ...
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In this paper, we introduce the concept of hexagonal cone b-metric spaces over Banach algebras as a generalization of cone hexagonal metric spaces and cone b-hexagonal metric spaces. An example is given at the end of the paper to show the applicability and validity of our results.
In this paper, we introduce the concept of algebra cone generalized b-metric space over Banach algebra by replacing the constant s >= 1 with r(s) >= 1 where r(s) is the spectral radius of s, with this modificati...
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In this paper, we introduce the concept of algebra cone generalized b-metric space over Banach algebra by replacing the constant s >= 1 with r(s) >= 1 where r(s) is the spectral radius of s, with this modification we shall prove Banach and Kannan fixed point results for contractive generalized Lipschitz mappings in such a space. Moreover, we present one example in support of our results.
The paper deals with the achievements of introducing the notion of F-cone metric spaces over Frechet algebra as a generalization of F-cone metric spaces over a Banach algebra, N-p-cone metric spaces over a Banach alge...
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The paper deals with the achievements of introducing the notion of F-cone metric spaces over Frechet algebra as a generalization of F-cone metric spaces over a Banach algebra, N-p-cone metric spaces over a Banach algebra, and N-b-cone metric spaces over a Banach algebra. First, we study some of its topological properties. Next, we define a generalized Lipschitz for such spaces. Also, we investigate some fixed points for mappings satisfying such conditions in the new framework. Subsequently, as an application of our results, we provide an example. Our work generalizes some well-known results in the literature.
In this paper, we obtain the existence of some common best proximity point theorems for generalized Lipschitz contractive mappings on cone b-metric spaces over Banach algebras without assumption of normality. Our resu...
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In this paper, we obtain the existence of some common best proximity point theorems for generalized Lipschitz contractive mappings on cone b-metric spaces over Banach algebras without assumption of normality. Our results generalize the corresponding result by Xu and Radenovic (Fixed Point Theory and Appl. 2014, 2014: 102) and by Huang and Radenovic (J. computational Anal. and Appl. 2016, 20(3)). Further, we give an example to illustrate that our works are never equivalent with the counterparts in the literature.
In the present paper, we first introduce the concept of cone b(2)-metric space over Banach algebras which generalizes the notions of b(2)-metric space and cone metric spaces over Banach algebra. Next, we define genera...
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In the present paper, we first introduce the concept of cone b(2)-metric space over Banach algebras which generalizes the notions of b(2)-metric space and cone metric spaces over Banach algebra. Next, we define generalized Lipschitz and expansive maps in the new structure and establish the existence and uniqueness of fixed points for such mappings in cone b(2)-metric space over Banach algebra. The results presented here generalize and extend some recent results of Singh et al. (comment Math 52(2):143-151, 2012) and Wang et al. (Math Japonica 29:631-636, 1984). Also, we illustrate the result by an appropriate example. Finally, an application to integral equations is given to demonstrate the effectiveness of our acquired results.
The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of Np-cone metric space over Banach algebra and Nb-cone metric space over Banach algebra a...
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In the present paper, we introduce the notion of A-cone metric spaces over Banach algebra as a generalization of A-metric spaces and cone metric spaces over Banach algebra. We also defined generalized Lipschitz and ex...
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In the present paper, we introduce the notion of A-cone metric spaces over Banach algebra as a generalization of A-metric spaces and cone metric spaces over Banach algebra. We also defined generalized Lipschitz and expansive maps in such maps and establish some fixed point theorems for such maps in the setting of the new space. As an application, we prove a theorem for integral equation. We provide illustrative example to verify our results. Our results generalize and unify some well-known results in the literature.
In our previously published papers [Monomial sequence of linear type, Illinois J. Math. 52 (2008) 1213-1221;sequences between d-sequences and sequences of linear type, comment. Math. Univ. carolin. 50 (2009) 1-9;Two-g...
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In our previously published papers [Monomial sequence of linear type, Illinois J. Math. 52 (2008) 1213-1221;sequences between d-sequences and sequences of linear type, comment. Math. Univ. carolin. 50 (2009) 1-9;Two-generated ideals of linear type, Acta Math. Univ. comenian. (N.S.) 78 (2009) 97-102] we have introduced and discussed the notion of a c-sequence in a commutative ring. In this paper we compare this notion with the notion of a d-sequence. The ideal generated by any of these sequences is of linear type. We show that there are c-sequences that are not d-sequences and that c-sequences satisfy analogs of sharp Artin-Rees properties that hold for d-sequences. We also discuss closeness of c and d-sequences.
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