TY - JOUR

T1 - Fuzzy Fixed Point Results in Convex C∗ -Algebra-Valued Metric Spaces

AU - Shagari, Mohammed Shehu

AU - Kanwal, Shazia

AU - Aydi, Hassen

AU - Gaba, Yaé Ulrich

N1 - Publisher Copyright:
© 2022 Mohammed Shehu Shagari et al.

PY - 2022

Y1 - 2022

N2 - The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C∗-algebra-valued fuzzy λ-contraction and related concepts in a convex C∗-algebra-valued metric space (C∗-AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approximate quantities is proposed. Consequently, two fixed point results of a C∗-algebra-valued fuzzy mapping (C∗-AVFM) for the new type of contractions are established using Mann and Ishikawa iterative schemes. For some future investigations of our results, two open problems are noted concerning sufficient criteria guaranteeing the existence of fixed points of a C∗-algebra-valued fuzzy λ-contraction and whether or not the Picard iteration for a C∗-algebra-valued fuzzy λ-contraction converges.

AB - The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C∗-algebra-valued fuzzy λ-contraction and related concepts in a convex C∗-algebra-valued metric space (C∗-AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approximate quantities is proposed. Consequently, two fixed point results of a C∗-algebra-valued fuzzy mapping (C∗-AVFM) for the new type of contractions are established using Mann and Ishikawa iterative schemes. For some future investigations of our results, two open problems are noted concerning sufficient criteria guaranteeing the existence of fixed points of a C∗-algebra-valued fuzzy λ-contraction and whether or not the Picard iteration for a C∗-algebra-valued fuzzy λ-contraction converges.

UR - http://www.scopus.com/inward/record.url?scp=85132646193&partnerID=8YFLogxK

U2 - 10.1155/2022/7075669

DO - 10.1155/2022/7075669

M3 - Article

AN - SCOPUS:85132646193

SN - 2314-8896

VL - 2022

JO - Journal of Function Spaces

JF - Journal of Function Spaces

M1 - 7075669

ER -