The Banach contraction principle in $C^{*}$-algebra-valued b-metric spaces with application

Kamran, Tayyab; Postolache, Mihai; Ghiura, Adrian; Batul, Samina; Ali, Rashid

doi:10.1186/s13663-015-0486-z

Cited by 33 publications

(17 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more details on other results from C * -algebra-cone metric spaces that is, from C * -algebra-cone b-metric spaces the reader can be see [40][41][42]44].…”

Section: Remarkmentioning

confidence: 99%

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

et al. 2020

View full text Add to dashboard Cite

We introduce the notion of α -admissibility of mappings on cone b-metric spaces using Banach algebra with coefficient s, and establish a result of the Hardy-Rogers theorem in these spaces. Furthermore, using symmetry, we derive many recent results as corollaries. As an application we prove certain fixed point results in partially ordered cone b-metric space using Banach algebra. Also, we use our results to derive and prove some real world problems to show the usability of our obtained results. Moreover, it is worth noticing that fixed point theorems for monotone operators in partially ordered metric spaces are widely investigated and have found various applications in differential, integral and matrix equations.

show abstract

“…For more details on other results from C * -algebra-cone metric spaces that is, from C * -algebra-cone b-metric spaces the reader can be see [40][41][42]44].…”

Section: Remarkmentioning

confidence: 99%

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

et al. 2020

View full text Add to dashboard Cite

show abstract

“…In [11], Caristi's …xed point theorem was given for C -algebra-valued metric spaces. Kamran et al [7] proved the Banach contraction principle in C -algebra-valued b-metric spaces with application. Bai [1] presented coupled …xed point theorems in C -algebra-valued bmetric spaces.…”

Section: Introductionmentioning

confidence: 99%

C^{∗}-algebra-valued rectangular b-metric spaces and some fixed point theorems

Kalpana¹,

Tasneem²

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

“…Kalaivani and Kalpana [3] considered the notion of C * -algebra valued b-metric spaces and obtained new contraction mapping gives an application to linear equation systems using such space. Kamran and his collabrates [4] generalized the new Banach contraction principle in C * -algebra-valued b-metric and obtained some result for an integral equation as application in a C * -algebra-valued b-metric space. Kang et all.…”

Section: Introductionmentioning

confidence: 99%

On the C ∗ -algebra valued G-metric space related with fixed point theorems

Özer¹,

Omran²

2019

Bul. Kar. Univ. - Math.

View full text Add to dashboard Cite

There are many fixed point results in the various kinds of metric spaces such as b-metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non-commutative Banach spaces etc. In this work, we consider the one of modern methods as C * -algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C * -algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result.

show abstract

The Banach contraction principle in $C^{*}$-algebra-valued b-metric spaces with application

Abstract: We introduce the notion of a C * -algebra-valued b-metric space. We generalize the Banach contraction principle in this new setting. As an application of our result, we establish an existence result for an integral equation in a C * -algebra-valued b-metric space.

Cited by 33 publications

References 8 publications

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

C^{∗}-algebra-valued rectangular b-metric spaces and some fixed point theorems

On the C ∗ -algebra valued G-metric space related with fixed point theorems

Contact Info

Product

Resources

About