Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings

A Self-Adaptive Shrinking Projection Method with an Inertial Technique for Split Common Null Point Problems in Banach Spaces

“…2. The result in this paper extends the results in [4,5,10,11] and several other results on solving split common null point problem from real Hilbert spaces to real Banach spaces. 3.…”

“…A significant improvement in this paper is that a self-adaptive technique is introduced for selecting the step size such that a strong convergence result is proved without prior knowledge of the norm of the bounded linear operator. This improves the results in [6,8,9,11,12,16,19,20] and other important results in this direction. 2.…”

“…We also prove a strong convergence result and provide some applications of our main theorem to solving other nonlinear optimization problems. This result improves and extends the results in [6,8,9,11,12,16,19,20] and many other recent results in the literature.…”

“…It is important to emphasize that the convergence of (4) is achieved with the aid of condition (3). Other similar results can be found, for instance, in [11,12] (and references therein). However, it is well known that the norm of bounded linear operator is very difficult to find (or at least estimate) (see [13][14][15]).…”

A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings

“…for all v ∈ D and u ∈ F ix(S) and (iii) demicontractive [12] if F ix(S) = ∅ and there exists η ∈ [0, 1) such that H(Su, Sv) 2 ≤ u − v 2 + ηd(v, Sv) 2 for all v ∈ D and u ∈ F ix(S). The class of multivalued demicontractive mappings contains properly the class of multivalued quasi-nonexpansive mappings [14].…”