A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings

CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators

“…It is shown that the existence of best proximity points for (EP)-mappings is equivalent to the existence of an approximate best proximity point sequence generated by a three-step iterative process. We also construct a CQ-type algorithm which generates a strongly convergent sequence to the best proximity point for a given (EP)-mapping.Symmetry 2020, 12, 4 2 of 11 TTP16), but for mappings satisfying the condition (E), introduced by García-Falset et al [5], extending Lemma 3.1 and, respectively, Theorem 3.2 from [12].Secondly, we adapt the iterative process TTP16 to the setting of non-self mappings and define a new class of operators which are required to have the (EP)-property (see below). This class includes proximal generalized nonexpansive mappings, introduced by Gabeleh [19].…”

A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces

“…(z (n) 1 , z (n) 2 ) = (1 − α n )(x (n) 1 , x (n) 2 ) + α n Rot n θ (x (n) 1 , x (n) 2 ) (y (n) 1 , y (n) 2 ) = (1 − β n )(z (n) 1 , z (n) 2 ) + β n Rot n θ (z (n) 1 , z (n) 2 ) (x (n+1) 1 , x (n+1) 2 ) = (1 − γ n )Rot n θ (z (n) 1 , z (n) 2 ) + γ n Rot n θ (y (n) 1 , y (n) 2 ) (22) Put α n = β n = γ n = 1 n + 100…”

“…By using MATHEMATICA, we computed the iterates of Algorithm (22) for initial point x (1) = ( 1 2 , 1 2 ) ∈ C for 500 steps. Finally, by the numerical experiments we compared Mann iteration process, Ishikawa iteration process and Thakur iteration process with our Algorithm (22) (see Table 2).…”

“…where {α n } ∞ n=1 is a sequence in (0, 1) and f is a φ-weak contraction on C. Further, in 2016, Balwant Singh Thakur, Dipti Thakur and Mihai Postolache in [22], introduced the following algorithm for nonexpansive mappings in uniformly convex Banach spaces:…”

Fixed point theorems for (L)-type mappings in complete CAT(0) spaces

“…In this section, we shall prove ∆ and strong convergence theorems for (L)-type mappings of a threestep iteration scheme introduced by Thakur et al in [29] which not only converges faster than the known iterations but also is stable. Give x 1 ∈ D, the sequence {x n } is generated by…”