Convergence theorems on asymptotically demicontractive and hemicontractivemappings in the intermediate sense

Abstract

In this study, we introduce two classes of nonlinear mappings,

Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

“…Let S be nonempty, bounded, closed, and convex subset of a real Hilbert space H. Let B 𝑗 ∶ S → H be a finite family of 𝜂 𝑗 -hemicontinuous and relaxed 𝜂 𝑗 − 𝜁 𝑗 monotone maps, 𝜑 𝑗 ∶ S × S → R be a finite family of bifunctions satisfying conditions (F1)-(F4) and g 𝑗 ∶ S → R be a finite family of proper, convex, and lower semicontinuous functions. Let T i ∶ S → S be a family of equally continuous maps that satisfy (7) and A i ∶ S → H be a family of maps defined in (10) with…”

“…Also, T is nonexpansive with 0 ∈ F(T) and consequently satisfies (7) with V n , r, k n = 0, and T n = T ∀n ∈ N. Also, A satisfies (10) with 𝜏 = 1 3 and 0 ∈ A −1 (0). The performance of our proposed Algorithm ( 36) is compared with that of the algorithms of Husain and Asad [23] and Harbau and Ahmad [51] with T 1 = T 2 = T, which are as follows, respectively,…”

Convergence and stability of modified multi-step Noor iterative procedure with errors for strictly hemicontractive-type mappings in Banach spaces

“…. , 10 and b (10) n = 5 9 • 1 √ n + 100 , c (10) n = 1 ( √ n + 100) 2 , a (10) n = 1b (10) n + c (10) n = 9n + 1795 √ n + 89,491 9( √ n + 100) 2 ,…”

“…Application of strictly hemicontractive-type mapping was initiated by Chidume and Osilike [4] for improving the consequence of Chidume [5]. After Chidume and Osilike [4], several researchers studied strictly hemicontractive-type mapping in many directions; see for instance [1][2][3][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references cited therein. Among the articles cited in [1][2][3][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], Hussain et al [1] studied Lipschitz strictly hemicontractive-type mapping in arbitrary Banach spaces to extend and improve the equivalent consequences of the monographs [4,5,[12][13][14]…”

Modified Noor iterations with errors for nonlinear equations in Banach spaces

“…Several authors in literature have obtained some interesting fixed points results (see, e.g. [1,7,8,12,13,21,19,24,26,27]). …”