Unique fixed point theorems for nonlinear mappings in Hilbert spaces (Q2925026)

A mapping \(T\) from a Hilbert space into itself is said to be \textit{symmetric more generalized hybrid} if there exist \(\alpha,\beta,\gamma,\delta,\zeta\in \mathbb{R}\) such that \(\alpha\|Tx-Ty\|^{2}+\beta(\|x-Ty\|^{2}+\|Tx-y\|^{2})+\gamma\|x-y\|^{2}+\delta(\|x-Tx\|^{2}+\|y-Ty\|^{2})+\zeta\|x-y-(Tx-Ty)\|^{2}\leq0\).NEWLINENEWLINEThe paper contains several unique fixed point theorems for symmetric more generalized hybrid mappings. The author also proves a unique fixed point result for strict pseudo-contractions and extends a result contained in [\textit{F. E. Browder}, Arch. Ration. Mech. Anal. 24, 82--90 (1967; Zbl 0148.13601)].