Let X be a Banach space and Z a relatively weakly compact subset of X. Let J : Z → R be a upper semicontinuous function bounded from above and p ≥ 1. This paper is concerned with the perturbed optimization problem of finding z0 ∈ Z such that ‖x− z0‖ + J(z0) = supz∈Z{‖x− z‖p + J(z)}, which is denoted by maxJ(x, Z). We prove in the present paper that if X is Kadec w.r.t. Z, then the set of all x ...

We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi-φ-asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proo...

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 ...

This article focuses on the maximum of relative projection constants over all m-dimensional subspaces of the N -dimensional coordinate space equipped with the max-norm. This quantity, called maximal relative projection constant, is studied in parallel with a lower bound, dubbed quasimaximal relative projection constant. Exploiting elegant expressions for these quantities, we show how they can b...

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, . . . , TN : K −→ E be N asymptotically nonexpansive nonself mappings with sequences {r n} such that ∑∞ n=1 r n < ∞, for all 1 ≤ i ≤ N and F = ∩i=1F (Ti) 6= φ. Let {α n}, {β n} and {γ n} are sequences in [0, 1] with α n + β i n + γ i n = 1 for all i =...

This article concerns the problem of stable recovering of any function in a shiftinvariant space from irregular samples of some filtered versions of the function itself. These samples arise as a perturbation of regular samples. The starting point is the generalized regular sampling theory which allows to recover any function f in a shiftinvariant space from the samples at {rn}n∈Z of s filtered ...