For example, an -generalized hybrid mapping is nonexpansive for α = 1 and β = 0, nonspreading for α = 2 and β = 1, and hybrid for α = 3 2 and β = 1 2. Recently, Maruyama et al. [10] defined a more general class of nonlinear mappings than the class of generalized hybrid mappings.
The derived stability conditions are used to analyze the stability of Takagi and Sugeno's fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems.
As interesting applications of the generalized Diaz-Margolis fixed point theorem, we establish some existence theorems of the Hyers-Ulam stability for a general class of the nonlinear Volterra integral equations in Banach spaces in Section 3.
As applications of the generalized Diaz-Margolis's fixed point theorem, we present some existence theorems of the Hyers-Ulam stability for a general class of the nonlinear Volterra integral equations in Banach spaces.
In 2006, Alber et al. [10] introduced a unified and generalized notion of a class of nonlinear mappings in Banach spaces, which can be introduced in the general setup of hyperbolic spaces as follows.
Inspired and motivated by recent research work in this field, in this paper, a new class of nonlinear generalized parametric ordered variational inclusions with - N O D S M mappings is studied in ordered Banach spaces.
Based on the multi-symplectic idea, a new theoretical framework named generalized multi-symplectic integrator for a class of nonlinear wave PDEs with small damping is proposed in this paper.
In 2010, Kocourek et al. [9] introduced a class of nonlinear mappings, say generalized hybrid mappings.
Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14 71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek et al. in Taiwan. J. Math. 14 2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20 197-228, 1967).
