The Retraction-Displacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm

Relevant Classes of Weakly Picard Operators

“…For more considerations on P O and W P O see: [38], [46], [3], [9], [13], [33], [35], [37], [39], [44], [45], [47], [48], . .…”

Local fixed point results for graphic contractions

“…is called a weakly ψ-Picard operator. For example, a graphic contraction with constant α ∈]0, 1[ is a weakly ψ-Picard operator with ψ(t) := 1 1−α t. Moreover, a Picard operator, with its unique fixed point denoted by x * ∈ X, for which there exists a function ψ : R + → R + increasing, continuous in 0 and satisfying ψ(0) = 0, such that…”

Saturated contraction principles for non self operators, generalizations and applications

“…The previous two theorems could now be unified to get a more general saturated principle for the class of nonself strict almost contractions, see also [13], [14], [53], [54], for more related developments.…”

“…For more considerations on data dependence problem, see also [5], [14], [21], [24], [53], [60], [62], [70],...…”

“…• Problem 1.3 and the retraction theory: [19], [65], [64], [62], [14], [32], [33], [36], [35], [41], [42], [43], [10], [61], [74], [28], . .…”