TY - JOUR
ID - 104146
TI - On one-local retract in modular metrics
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Olela Otafudu, Oliver
AU - Phawe, Tlotlo Odacious
AD - School of Mathematical and Statistical Sciences
North-West University, Potchefstroom Campus,
Potchefstroom 2520,
South Africa.
Y1 - 2024
PY - 2024
VL - 20
IS - 1
SP - 201
EP - 220
KW - fixed point
KW - one local retract
KW - normal structure
KW - $w$-admissible
DO - 10.48308/cgasa.2023.234064.1451
N2 - We continue the study of the concept of one local retract in the settings of modular metrics. This concept has been studied in metric spaces and quasi-metric spaces by different authors with different motivations. In this article, we extend the well-known results on one-local retract in metric point of view to the framework of modular metrics. In particular, we show that any self-map $\psi: X_w \longrightarrow X_w$ satisfying the property $w(\lambda,\psi(x),\psi(y)) \leq w(\lambda,x,y)$ for all $x,y \in X$ and $\lambda >0$, has at least one fixed point whenever the collection of all $q_w$-admissible subsets of $X_{w}$ is both compact and normal.
UR - https://cgasa.sbu.ac.ir/article_104146.html
L1 - https://cgasa.sbu.ac.ir/article_104146_511c297d30e90fabece4a56eab1d2ef8.pdf
ER -