An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

Abstract

<abstract><p>In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of $ \Bbbk $-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. Theoretical results comprise strong convergence characteristics under suitable sets of constraints as well as numerical results are established for the underlying algorithm. Applications to signal processing as well as various abstract problems are also incorporated.</p></abstract>

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

“…For other related developments on this topic, we refer the readers to Maingé [19], who obtained common fixed-point convergence results by extending Mȃruşter's convergence theorem (Theorem 1) from one demicontractive mapping to a finite family of demicontractive mappings in a Hilbert space; Adamu and Adam [30]; Arfat et al [31], where the authors investigate a fixed-point problem involving an infinite family of k-demicontractive operators in conjunction with the split common null point problems (SCNPP) in Hilbert spaces by using an accelerated variant of the hybrid shrinking projection algorithm; Maingé and Mȃruşter [32]; Anh et al [33]; Charoensawan and Suparatulatorn [34]; Lin [35]; Mongkolkeha et al [36]; Wang et al [37]; Xiao et al [38]; Zhu and Yao [39], etc.…”

“…From the diversity of nonlinear problems that were solved in connection with the class of demicontractive mappings, we shall expose in more details only two of them, namely, the variational inequality problems and equilibrium problems. For other problems, namely for minimization problems, we refer to Arfat et al [31] and Chang et al [101].…”

“…We end this section by mentioning another important application of the above results to convex minimization over the fixed-point set of demicontractive mappings (a topic which is not reviewed here); see Maingé [21], Mewomo [128], Okeke et al [109], Chang et al [101], Jailoka et al [129], Arfat et al [31], etc.…”