In this paper, we introduce a new geometric property (UÃ2) and we show that if a separable Banach space has this property, then both X and its dual X∗ have the weak fixed point property. We also prove that a uniformly Gateaux differentiable Banach space has property (UÃ2) and that if X∗ has property (UÃ2), then X has the (UKK)-property. Criteria for Orlicz spaces to have the properties (UA2), (...

‎the purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex banach space which has a‎ ‎uniformly g^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

exists for each x, y ∈ S(E). In this case E is called smooth. The norm of E is said to be Fréchet differentiable if for each x ∈ S(E) the limit is attained uniformly for y ∈ S(E). The normofE is called uniformlyFréchet differentiable if the limit is attained uniformly for x, y ∈ S(E). It is well known that (uniform) Fréchet differentiability of the norm of E implies (uniform) Gâteaux differenti...

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

We find an expression for the Gateaux derivative of C⁎-algebra norm. Using this, we obtain a characterization orthogonality operator A∈B(H,K) to subspace, under assumption dist(A,K(H,K))<‖A‖. subdifferential set norm function at A∈B(H) when dist(A,K(H))<‖A‖. also give new proofs known results on closely related notions smooth points and Birkhoff-James spaces B(H) Cb(Ω), respectively.

In this paper, we prove a convergence theorem for Passty type asymptotically nonexpansive mappings in a uniformly convex Banach space with Fréchet-differentiable norm.

The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to λ-strict pseudocontractions in p-uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.