Abstract In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied uniformly convex 2-uniformly smooth real Banach space with Opial property best smoothness constant κ satisfying condition $0&lt;\kappa &lt; \frac{1}{\sqrt{2}}$ <mml:math xmlns:mml="http://ww...

Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that P∞ n=1(kn − 1) < ∞ and let F (T ) be nonempty, where F (T ) denotes the fixed points set of T . Let {αn}, {βn}, {γn}, {αn}, {β′ n}, {γ′ n}, {α′′ n}, {β′′ n} and {γ′′ n} be real sequen...

We begin by considering second order dynamical systems of the from ẍ(t) + Γ(ẋ(t)) + λ(t)B(x(t)) = 0, where Γ : H → H is an elliptic bounded self-adjoint linear operator defined on a real Hilbert space H, B : H → H is a cocoercive operator and λ : [0,+∞)→ [0,+∞) is a relaxation function depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cau...

Abstract The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework p -vector spaces, in particular, locally -convex spaces $0 &lt; \leq 1$ 0&lt;p≤1 . More precisely, ba...