Some new results for Reich type mappings on cone b-metric spaces over Banach algebras

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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“…Examples are also given to elucidate our results. Our results extend and generalize many results in [1,[3][4][5][6][7][8][9][10].…”

Section: Introductionsupporting

confidence: 88%

Some Fixed Point Theorems of Contractive Mappings in $P_{b}^{r}$ -Cone Metric Spaces over Banach Algebras

Auwalu

Hınçal

2021

Journal of Mathematics

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“…(iii) If we take s(x, y) = b for some b ≥ 1 in Theorems 3.7 and 3.9, we obtain the main results of [27] for cone b-metric spaces over a Banach algebra.…”

Section: Example 38 Letmentioning

confidence: 77%

Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results

et al. 2022

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In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type space. We introduce a new metric space and prove analogs of Banach-, Kannan- and Reich-type fixed-point theorems. We also furnish various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in the literature.

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“…Definition 23. (see [37]). Let a cone b 2 -metric space be ðX, ∂Þ over the Banach algebra B with parameter b, ðb ⪰ eÞ, C B be a solid cone, α : X × X × X ⟶ C B , and d : X ⟶ X be two mappings.…”

Section: Lemma 22mentioning

confidence: 96%

Fixed-Point Results for Generalized $α$ -Admissible Hardy-Rogers’ Contractions in Cone $b_{2}$

Islam

Sarwar

Sen

2020

Advances in Mathematical Physics

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In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

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Some new results for Reich type mappings on cone b-metric spaces over Banach algebras

Cited by 5 publications

References 12 publications

Some Fixed Point Theorems of Contractive Mappings in $P_{b}^{r}$ -Cone Metric Spaces over Banach Algebras

Some Fixed Point Theorems of Contractive Mappings in $P_{b}^{r}$ -Cone Metric Spaces over Banach Algebras

Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results

Fixed-Point Results for Generalized $α$ -Admissible Hardy-Rogers’ Contractions in Cone $b_{2}$

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Some new results for Reich type mappings on cone b-metric spaces over Banach algebras

Cited by 5 publications

References 12 publications

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

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

Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results

Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2

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Product

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Some Fixed Point Theorems of Contractive Mappings in $P_{b}^{r}$ -Cone Metric Spaces over Banach Algebras

Some Fixed Point Theorems of Contractive Mappings in $P_{b}^{r}$ -Cone Metric Spaces over Banach Algebras

Fixed-Point Results for Generalized $α$ -Admissible Hardy-Rogers’ Contractions in Cone $b_{2}$