Some fixed point theorems in C^* -algebra valued b -metric spaces

Subject Areas : Statistics

zahra  ghorbani ¹ (Department of mathematics, Jahrom university)
javad  baradaran ² (Department of Mathematics, Jahrom University, Jahrom, Iran)

Received: 2019-05-02 Accepted : 2019-09-21 Published : 2020-12-21

Keywords: نقطه تناوبی, فضای -bمتریک - C*جبر-مقدا, نقطه ثابت, - پیوسته مداری,

Abstract :

In this paper, we first define the notions of orbitally continuous and orbitally complete on a C*-algebra-valued metric space. We show that if T is an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d), where X is a nonempty set and A is a C*-algebra with the relation ⪯ and if T orbitally complete and satisfies some conditions, then for any x∈X the iterated sequence {Tn (x)} converges to a fixed point of T. Also, we prove that an orbitally continuous mapping on a C*-algebra-valued metric space (X,A, d) under conditions has a periodic point. It is prove that an orbitally continuous self-map on a C*-algebra-valued b-metric space (X,A, d) under which conditions has at least a fixed point. In additions, if (X,A, d) be a complete C*-algebra-valued metric space and T has some property. Then T has a fixed point in X provided that there exists x0∈X such that T2 (x0)≠x

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