On analytical and numerical study of implicit fixed point iterations

Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

“…Then the iterative algorithm (33) converges to the fixed point x * of S and x * is the unique solution of nonlinear variational inclusion problem (8).…”

“…Chugh and Kumar [7] studied strong convergence and almost stability of SP iterative algorithm with mixed errors for the accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach spaces. Recently, Chugh et al [8] and Hussain et al [12] proved some strong convergence results of iterative algorithms. In computational mathematics, a fixed point iterative algorithm is valuable and useful for applications if it satisfies the following conditions:…”

An investigation of new quicker implicit iterations in hyperbolic spaces

“…Iterative fixed points procedures in convex distance spaces have been obtained by many researchers, see, e. g., [6][7][8][9], using implicit iterative procedures which are incredible significance from numerical angle as they give precise estimate…”

Convergence Rate of Implicit Iteration Process and a Data Dependence Result

“…Every hyperbolic space is a convex metric space but converse does not hold in general ( [6]). A subset E of a W −hyperbolic space X is convex if W (x, y, α) ∈ E for all x, y ∈ E and α ∈ [0, 1].…”

“…Implicit iterative schemes are of great importance from numerical stand point as they provide accurate approximation ( see, [6], [12], [7,8,20]). …”