$ \alpha $-Admissible mapping in $ C^{*} $-algebra-valued b-metric spaces and fixed point theorems

Saleh Omran; Ibtisam Masmali; Saleh Omran; Ibtisam Masmali

doi:10.3934/math.2021590

AIMS Mathematics

2021, Volume 6, Issue 9: 10192-10206. doi: 10.3934/math.2021590

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$ \alpha $-Admissible mapping in $ C^{*} $-algebra-valued b-metric spaces and fixed point theorems

Saleh Omran ¹,
Ibtisam Masmali ^{2
,
,}

1.
Department of Mathematics, South Valley University, Qena 83523, Egypt
2.
Department of Mathematics, College of Science, Jazan University, New Campus, Post Box 2097, Jazan, Saudi Arabia

Received: 02 April 2021 Accepted: 18 June 2021 Published: 09 July 2021
MSC : 47H10, 46L07

In the present paper, for a unital $ C^* $-algebra A, we introduce a version of $ \alpha_A $-admissible on $ C^* $-algebra-valued b-metric space, we proved some Banach and common fixed point theorems using $ \alpha_A $-admissible. Also, we give some non-trivial examples and an application to illustrate our results.
- $ C^{*} $-algebra-valued b-metric space,
- fixed point theorem,
- $ \alpha $-admissible
Citation: Saleh Omran, Ibtisam Masmali. $ \alpha $-Admissible mapping in $ C^{*} $-algebra-valued b-metric spaces and fixed point theorems[J]. AIMS Mathematics, 2021, 6(9): 10192-10206. doi: 10.3934/math.2021590

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Abstract

In the present paper, for a unital $ C^* $-algebra A, we introduce a version of $ \alpha_A $-admissible on $ C^* $-algebra-valued b-metric space, we proved some Banach and common fixed point theorems using $ \alpha_A $-admissible. Also, we give some non-trivial examples and an application to illustrate our results.

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