Convergence theorems for new classes of multivalued hemicontractive-type mappings

Abstract

Weak and strong convergence theorems are proved in Hilbert spaces for new classes of multivalued demicontractive-type and hemicontractive-type mappings which are related to the class of multivalued pseudocontractive-type mappings studied by Isiogugu (Fixed Point Theory Appl. 2013:61, 2013). Thus our results extend and improve several corresponding results in the contemporary literature. MSC: 47H10; 54H25

Strong andΔ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0)Spaces

“…Thus, our result is applicable to all classes of demicontractive mappings. Furthermore, our theorems extend and improve the results of Chidume and Ezeora [18], Chidume et al [17], and Isiogugu and Osilike [19] and complement the results of Dhompongsa and Panyanak [16], Dhompongsa et al [9], Leustean [11], Shahzad and Markin [13], and Sokhuma [20] and results of a host of other authors on iterative approximation of fixed points in CAT(0) spaces.…”

“…In [19], Isiogugu and Osilike proved weak and strong convergence theorems for the class of multivalued demicontractive mappings which contains the class of -strictly pseudocontractive mappings for which the fixed point set ( ) is nonempty. They proved the following theorem in the setting of real Hilbert spaces.…”

Algorithms of common solutions for a fixed point of hemicontractive-type mapping and a generalized equilibrium problem

“…Several authors have studied iterative algorithms for approximating fixed points of various classes of nonlinear mappings (including hemicontractive mapping); see, for example, [5,8,14,15,21] and the references cited therein. In 2007, Rafiq [13] introduced the following Mann-type implicit iteration process and showed that the process converges strongly to a fixed point of a continuous hemicontractive mapping T from a compact and convex subset C of a real Hilbert space into itself:…”

“…In the case of F ≡ 0, then the problem (1.6) reduced to finding z ∈ C such that 8) which is called the classical variational inequality problem. The set of solutions of problem (1.8) is denoted by V I(C, A).…”

A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

“…On the other hand, the approximation of fixed points of multivalued mappings with respect to Hausdorff metric has been an area of great research interest due to its numerous applications in diverse areas such as game theory, mathematical economics, non-smooth differential equations and others. Thus, it has continued to attract the interest of numerous researchers (see, for example [4,19,30]). Recently, Chidume and Ezeora [13] introduced and studied a Krasnoselskii-type algorithm, and proved its strong convergence to a common fixed point of a finite family of multivalued strictly pseudocontractive mappings in a real Hilbert space.…”