@article{Singh2024, 
author = {Moirangthem Pradeep Singh and Yumnam Rohen and Khairul Habib Alam and Junaid Ahmad and Walid Emam},
title = {On fixed point and an application of        C    ∗  -algebra valued    (  α  ,  β  )-Bianchini-Grandolfi gauge contractions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15172-15189},
keywords = {Bianchini-Grandolfi gauge function, gauge function, C∗-algebra valued, (α, β)-Bianchini-Grandolfi gauge contraction},
url = {https://www.sciopen.com/article/10.3934/math.2024736},
doi = {10.3934/math.2024736},
abstract = {It is the purpose of the present paper to obtain certain fixed point outcomes in the sense of        C    ∗  -algebra valued metric spaces. Here, we present the definitions of the gauge function, the Bianchini-Grandolfi gauge function,    α-admissibility, and    (  α  ,  β  )-admissible Geraghty contractive mapping in the sense of        C    ∗  -algebra. Using these definitions, we define    (  α  ,  β  )-Bianchini-Grandolfi gauge contraction of type I and type II. Next, we prove our primary results that the function satisfying our contraction condition has to have a unique fixed point. We also explain our results using examples. Additionally, we discuss some consequent results that can be easily obtained from our primary outcomes. Finally, there is a useful application to integral calculus.}
}