$n$-tuple ‎F‎ixed Point Theorems Via $\alpha$-series in $C^*$-algebra-valued Metric Spaces with an Application in Integral Equations

Subject Areas : International Journal of Industrial Mathematics

سمیرا هادی بناب ¹ , وحید پروانه ² , حسن حسین زاده ³ , حسن آیدی ⁴ , سید جلالدین حسینی غنچه ⁵

1 - Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
2 - Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
3 - Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
4 - Universit\'e de Sousse, Institut Sup\'erieur d'Informatique et des Techniques de Communication, H.~Sousse~4000, Tunisia.
5 - Department of Mathematics, Takestan Branch Islamic Azad University, Takestan, Iran.

Received: 2021-08-12 Accepted : 2022-10-09 Published : 2023-07-01

Keywords: $alpha$-series, $C^*$-algebra-valued metric space, $n$-tuple fixed point, $n$-tuple coincidence point, Compatible mappings, Weakly reciprocally continuous mappings,

Abstract :

The purpose of this paper is to present some $n$-tuple fixed point and $n$-tuple coincidence point results in $C*$-algebra-valued metric spaces using the concept of an $\alpha$-series applied to a series of mappings. At the end of the paper, we give an example and an application to support our main results.