Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity

The Viscosity Subdiierential of the Sum of Two Functions in Banach Spaces I: First Order Case

We present a formula for the viscosity subdiierential of the sum of two uniformly continuous functions on smooth Banach spaces. This formula is deduced from a new variational principle with constraints. We obtain as a consequence a weak form of Preiss' theorem for uniformly continuous functions. We use these results to give simple proofs of some uniqueness results of viscosity solutions of Hami...

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in...

Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality probl...