TY - JOUR

T1 - Fixed point theorem with contractive mapping on C∗-Algebra valued G-metric space

AU - Wijaya, A.

AU - Hariadi, N.

N1 - Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.

PY - 2021/11/23

Y1 - 2021/11/23

N2 - Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T: X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C∗-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C∗-algebra valued G-metric space is a generalization of the G-metric space and the C∗-algebra valued metric space, meanwhile the G-metric space and the C∗-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X×X into X×X×X, the C∗-algebra valued metric generalized the codomain from real number into C∗-algebra, and the C∗-algebra valued G-metric space generalized both the domain and the codomain. In C∗-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C∗-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)g.

AB - Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T: X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C∗-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C∗-algebra valued G-metric space is a generalization of the G-metric space and the C∗-algebra valued metric space, meanwhile the G-metric space and the C∗-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X×X into X×X×X, the C∗-algebra valued metric generalized the codomain from real number into C∗-algebra, and the C∗-algebra valued G-metric space generalized both the domain and the codomain. In C∗-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C∗-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)g.

UR - http://www.scopus.com/inward/record.url?scp=85121446788&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/2106/1/012015

DO - 10.1088/1742-6596/2106/1/012015

M3 - Conference article

AN - SCOPUS:85121446788

SN - 1742-6588

VL - 2106

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012015

T2 - International Conference on Mathematical and Statistical Sciences 2021, ICMSS 2021

Y2 - 15 September 2021 through 16 September 2021

ER -