Fixed point theorems for generalized \((\alpha,\beta)\)-\(S\)-Nonexpansive mappings without demi-closedness principle in Banach spaces
Applicable Nonlinear Analysis, Volume 3, Issue 3, December 2026, Pages: 164–175
Eskandar Naraghirad
Department of Mathematics, Faculty of Sciences, Yasouj University, Yasouj 75918, Iran
Abstract
We introduce a new class of nonlinear mappings called generalized \((\alpha,\beta)\)-\(S\)-nonexpansive mappings and show that this class of nonlinear mappings can be considered as an extension of of nonexpansive, firmly-nonexpansive and \((\alpha,\beta)$-nonexpansive mappings. Beyond the continuity assumption on the mappings and without using the classical demiclosedness principle, we will verify new existence and convergence results for these mappings in Banach spaces. To illustrate the results, we include some examples in the paper.
Cite this Article as
Eskandar Naraghirad, Fixed point theorems for generalized \((\alpha,\beta)\)-\(S\) -Nonexpansive mappings without demi-closedness principle in Banach spaces, Applicable Nonlinear Analysis, 3(3), 164–175, 2026