Demiclosedness and weak convergence of supper hybrid mappings in Banach spaces

Ezugorie, Ikechukwu Godwin (2025) Demiclosedness and weak convergence of supper hybrid mappings in Banach spaces. World Journal of Advanced Research and Reviews, 27 (2). pp. 1564-1570. ISSN 2581-9615

We introduce and study a new class of mapping in Banach Spaces, termed (α , β,γ) - supper hybrid mappings, which generalize the well – known ( α , β ) - generalized hybrid mappings. This extended framework encompasses a broader spectrum of nonlinear of nonlinear operators and allows for refined control via an additional parameter γ ≥ 0. We establish several foundational properties of supper hybrid mappings, including quasi – nonexpansivenes and the demiclosedness principle at zero. Furthermore, we prove a nonlinear ergodic theorem of Baillon’s type in Hilbert spaces for supper hybrid mappings, demonstrated weak convergence of the Cesàro means to a fixed point. Our approach leverages metric projections and techniques inspired by Takahashi, thereby extending classical fixed point theory to this new operator class.