We prove that if K is a Gruenhage compact space then C (K) admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X∗ = span|||·|||(K), where K is a Gruenhage compact in the w∗-topology and ||| · ||| is equivalent to a coarser, w∗-lower semicontinuous norm on X∗, then X∗ admits an equivalent, strictly convex dual norm. We give a partial converse ...

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

This paper contains the following results for ecohomies with infinite dimensional commodity spaces. (i) We establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Schmeidler-Hildenbrand [Hi...

We prove that Banach spaces ℓ1 ⊕2 R and X ⊕∞ Y , with strictly convex have plastic unit balls (we call a metric space if every non-expansive bijection from this onto itself is an isometry).

and Applied Analysis 3 Theorem 1.3. Let E be a real q-uniformly smooth Banach space which is also uniformly convex, let C be a nonempty closed convex subset of E, let T : C → C be a (λ, {kn})-strictly asymptotically pseudocontractive mapping such that ∑∞ n 1 k 2 n − 1 < ∞, and let F T / ∅. Let {αn} ⊂ 0, 1 be a real sequence satisfying the following condition: 0 < a ≤ αn ≤ b < q 1 − k 2cq 1 L − ...

and Applied Analysis 3 for each x, y ∈ U. It is also said to be uniformly smooth if the limit is attainted uniformly for each x, y ∈ U. It is well known that ifE is smooth, then the dualitymapping J is single valued. It is also known that if E is uniformly smooth, then J is uniformly norm-to-norm continuous on each bounded subset ofE. Someproperties of the dualitymapping have been given in [22]...

Let B (resp. K , BC , K C ) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B stand for the set of all F ∈ B such that the problem (F,G) is well-posed. We proved that, if X is strictly convex and Kadec, the set ...

We introduce an iterative scheme for finding a common element of the set of solutions of generalizedmixed equilibrium problems and the set of fixed points for countable families of total quasi-φasymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly co...