Dr. Chaimaa Benzarouala is an Assistant Professor of Mathematics at the Faculty of Sciences, El Jadida, Morocco. She earned her Ph.D. in Mathematics from Mohammed V University, Rabat, where her research focused on functional analysis, nonlinear analysis, and their applications. Her doctoral work, titled “Stability and Hyperstability of Functional Equations,” explores Ulam stability in various mathematical frameworks, including Banach spaces and random normed spaces, using advanced fixed point methods. Her research contributions extend to generalized functional equations, gauge spaces, and delay differential equations. Dr. Benzarouala has authored numerous peer-reviewed publications in reputable international journals, with a strong emphasis on fixed point theory, Ulam–Hyers–Rassias stability, and fractional differential equations. Her work has significantly contributed to the theoretical development and applications of stability analysis in modern mathematics. She has presented her research at several international conferences and workshops across Europe and North Africa, highlighting her active engagement with the global mathematical community. In addition to her research, Dr. Benzarouala has extensive teaching experience, having taught courses in algebra, analysis, statistics, operations research, and linear programming at both undergraduate and engineering levels.

A fixed point theorem in gauge spaces and applications to Ulam-stability of delay differential equationsDuring this talk, we prove a new alternative fixed point theorem in generalized gauge (or generalized uniformizable) spaces. This is a generalization of a famous result of Diaz-Margolis. Next, using this theorem, we show the stability of the following delay differential equation                                                                            y ′ (t) = F(t,y(t),y(g(t))), t ∈ I ⊂ R,where the unknown mapping y takes its values in a locally convex space. Examples are given to support our results.