Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality

In this paper, we discuss and obtain some new unique common fixed point theorems for two mappings satisfying Kannan type mixed contractive conditions and Chatterjea type mixed contractive conditions respectively on cone metric spaces over Banach algebras without the assumption of normality and give some generalizations of Kannan type and Chatterjea type fixed point theorems.

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Ciric type fixed point theorems under c-distance on non-normal cone metric spaces over Banach algebras

Advances in Fixed Point Theory ◽

10.28919/afpt/4444 ◽

2020 ◽

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Normal Cone ◽

Metric Spaces ◽

Banach Algebras ◽

Cone Metric Spaces ◽

Cone Metric

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Some Fixed Point Theorems of Contractive Mappings in P b r -Cone Metric Spaces over Banach Algebras

Journal of Mathematics ◽

10.1155/2021/8447435 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Abba Auwalu ◽

Evren Hinçal

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Banach Algebras ◽

Cone Metric Space ◽

Cone Metric Spaces ◽

Contractive Mappings ◽

Cone Metric

In this paper, we introduce the concept of a P b r -cone metric space over Banach algebras and prove some fixed point results under various contractive mappings in such a space. Some examples are given to elucidate the results. Our results extend and generalize many existing results in the literature.

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Cone Metric Spaces over Topological Modules and Fixed Point Theorems for Lipschitz Mappings

Mathematics ◽

10.3390/math8050724 ◽

2020 ◽

Vol 8 (5) ◽

pp. 724

Author(s):

Adrian Nicolae Branga ◽

Ion Marian Olaru

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Cone Metric Space ◽

Left Module ◽

Cone Metric Spaces ◽

Lipschitz Mappings ◽

Topological Modules ◽

Cone Metric

In this paper, we introduce the concept of cone metric space over a topological left module and we establish some coincidence and common fixed point theorems for self-mappings satisfying a condition of Lipschitz type. The main results of this paper provide extensions as well as substantial generalizations and improvements of several well known results in the recent literature. In addition, the paper contains an example which shows that our main results are applicable on a non-metrizable cone metric space over a topological left module. The article proves that fixed point theorems in the framework of cone metric spaces over a topological left module are more effective and more fertile than standard results presented in cone metric spaces over a Banach algebra.

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Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras

Journal of Function Spaces ◽

10.1155/2018/9395057 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8

Author(s):

Seong-Hoon Cho

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Banach Algebras ◽

Weak Contraction ◽

Cone Metric Spaces ◽

Contraction Type ◽

Cone Metric

The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. An example to illustrate main theorem is given. Finally, applications of our main result to cyclic mappings and weak contraction type mappings are given.

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Some fixed point results on $\mathcal{N}_{b}$-cone metric spaces over Banach algebra

Advances in Difference Equations ◽

10.1186/s13662-020-02991-5 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Jerolina Fernandez ◽

Neeraj Malviya ◽

Zoran D. Mitrović ◽

Azhar Hussain ◽

Vahid Parvaneh

Keyword(s):

Fixed Point ◽

Banach Algebra ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Cone Metric Spaces ◽

Coupled Common Fixed Point ◽

Lipschitz Mappings ◽

Special Cases ◽

Common Fixed Point Theorems ◽

Cone Metric

Abstract The main aim of this paper is to introduce the concept of $\mathcal{N}_{b}$ N b -cone metric spaces over a Banach algebra as a generalization of $\mathcal{N}$ 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.

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