We propose the class of uniformly convex W -hyperbolic spaces with monotone modulus of uniform convexity (UCW -hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive iterations. UCW -hyperbolic spaces are a natural generalization both of uniformly convex normed spaces and CAT (0)-spaces. Furthermore, we apply proof mining techniques to get effective rates of asympt...

*Correspondence: [email protected]; [email protected] Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {Tn} : C→ C be a countable family of weak relatively nonexpansive mappings such that F = ⋂∞ n=1 F(Tn) = ∅. For any given gauss x0 ∈ C,...

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary sufficient Pareto optimality conditions for considered under some constraint qualifications. These results are motivated by the symmetric obtained recent article Cobos Sánchez et al. 2021 on of continuous linear operators. The ...

and Applied Analysis 3 It is shown in [19] that if E = H, a real Hilbert space, then ρ(t) = t, for t > 0. In our general setting, throughout this paper we assume that ρ(t) ≤ 2t. Lemma 3. Let E be a real Banach space. Then the following inequality holds: 󵄩󵄩󵄩󵄩x + y 󵄩󵄩󵄩󵄩 2 ≤ ‖x‖ 2 + ⟨y, j (x + y)⟩ , ∀x, y ∈ H, j (x + y) ∈ J (x + y) . (10) Lemma 4 (see [20]). Let E be a uniformly convex Banach spac...

We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a ...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...

1. A few years ago Rogers [1] showed that, if K is any convex body in n-dimensional Euclidian space, there is a covering of the whole space by translates of K with density less than nlogn+nloglogn+5n, provided n > 3. However the fact that the covering density is reasonably small does not imply that the maximum multiplicity is also small. In the natural covering of space by closed cubes, the den...