The most popular technique of proving the stability of functional equations except for direct method is the fixed point method [16, 20 23].
for all u, a, b, c, x1, x2,..., x m ∈ A. By using the same technique of proving Corollary 2.4, we can prove the Isac-Rassias type stability of ternary derivations on ternary quasi-Banach algebras as follows.
(b) The technique of proving weak convergence in Theorem 3.1 is different from that in [[8], Theorem 5.7] because our technique uses asymptotically quasi-nonexpansive mappings and the property of maximal monotone mappings.
(b) The technique of proving weak convergence in Theorem 3.1 is different from that in [[7], Theorem 5.7] because of our technique to use asymptotically quasi-nonexpansive mappings and the property of maximal monotone mappings.
The technique of proving weak convergence in Theorem 3.1 is different from that in [[8], Theorem 5.7] because our technique uses asymptotically quasi-nonexpansive mappings and the property of maximal monotone mappings.
The technique of proving weak convergence in Theorem 3.1 is different from those in [15], Theorem 3.6 and [23], Theorem 3.2 because our technique depends only on the demiclosedness principle for pseudo-contractive mappings in Hilbert spaces.
The technique of proving weak convergence in Theorem 4.1 is different from those in [15], Theorem 3.6 and [23], Theorem 3.2 because our technique depends on the demiclosedness principle for pseudo-contractive mappings and bases on condition (2.5) in Hilbert spaces.
Then there exists a unique ternary derivation D : A → B such that f ( x ) - D ( x ) ≤ [ Ψ ( x ) ] 1 p. for all x ∈ A. Proof: By using the same technique of proving Theorem 2.1, the limit lim n → ∞ 1 m n f ( m n x ).
The first one was often used in the context of Fejer monotonicity techniques for proving convergence results of classical algorithms for convex optimization problems or, more generally, for monotone inclusion problems (see [17]).
The nanoparticles and nanocomposite thus synthesized were passed through a series of techniques to prove the authenticity of their quality, quantity and to understand the nanostructure dynamics in the aqueous extract.
