Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type.
In this paper, we prove strong convergence of a path for a convex combination
of a pseudocontractive type of operators in a real reflexive Banach space
having a weakly continuous duality mapping J? with gauge function ?. Using
path convergency, we establish strong convergence of an implicit iterative
algorithm for a pseudocontractive mapping combined with a strongly
pseudocontractive mapping in the same Banach space.
The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operatorsU,T, and xn=αnfxn+1-αnUλxn-ρnA*I-TAxn,n≥0, whereUλ=(1-λ)I+λU, and we obtain the sequence which strongly converges to a solutionx^of this problem, and the solutionx^satisfies the variational inequality.〈x^-f(x^),x^-z〉≤0,∀z∈S, whereSdenotes the set of all solutions of the split common fixed point problem.
Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods
