2016
DOI: 10.1155/2016/9217091
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Stability for a New Class of GNOVI with (γG,λ)-Weak-GRD Mappings in Positive Hilbert Spaces

Abstract: By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions) with ( , )-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained. Preliminaries and a New Class of GNOVI StructuresLet us recall … Show more

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Cited by 3 publications
(7 citation statements)
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“…It is clear that, for suitable choices of mappings involved in the formulation of nonlinear fuzzy ordered variational inclusion problem (3.1), one can obtain many variational inclusion problems studied in recent past, i.e., [17][18][19]25].…”
Section: Lemma 217mentioning
confidence: 99%
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“…It is clear that, for suitable choices of mappings involved in the formulation of nonlinear fuzzy ordered variational inclusion problem (3.1), one can obtain many variational inclusion problems studied in recent past, i.e., [17][18][19]25].…”
Section: Lemma 217mentioning
confidence: 99%
“…Putting a(p) = b(p) = c(p) = d(p) = 1 for all p ∈ H p , problem (3.1) includes many kinds of variational inequalities and variational inclusion problems [17,19,[22][23][24][25].…”
Section: Lemma 217mentioning
confidence: 99%
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“…Problem (13) was examined by Li et al [25]. (iv) If ϕ(•, •) = 0 and P = 0, then problem (11) becomes an equivalent problem of finding…”
Section: Formulation Of the Problem And Existence Resultsmentioning
confidence: 99%
“…In [24], Li et al investigated the solution of a general nonlinear ordered variational inclusion with (γ G , λ)-weak-GRD mappings. Recently, Li et al [25] presented the convergence of an Ishikawa-type iterative method for the general nonlinear ordered variational inclusion with (γ G , λ)-weak-GRD set-valued mappings, and exhibited the stability of the algorithm. Very recently, ordered variational inclusions with XOR operator are considered in diverse direction-see, for example, [26,27].…”
Section: Introductionmentioning
confidence: 99%