and Applied Analysis 3 that the function f : (X, α) → (Y, β) is strongly proximally continuous on A if ∀E ⊂ A, ∀S ⊂ X, EαS 󳨐⇒ f (E) βf (S) . (5) Finally, one says that f is strongly proximally continuous on B if f is strongly proximally continuous on A, for every A ∈ B. We shall use the notation C B (X, Y) to denote the family of the functions from X to Y which are strongly proximally continuou...

in this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in hilbert space. a strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. the main result of this paper extendthe results obtain...

Abstract We correct a logic mistake in our paper “On statistical convergence and strong Cesàro by moduli” (León-Saavedra et al. J. Inequal. Appl. 23:298, 2019).

in this paper, we prove the existence of fi xed point for j-type multi-valuedmap t in cat(0) spaces and also we prove the strong convergence theoremsfor ishikawa iteration scheme without using the xed point of involving map.