Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov i...

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the ...

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

‎In this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex Banach space‎. ‎The results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...