Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator

Ahmad, I.; Rahaman, Mijanur; Ahmad, Rais; Ali, Ihsan

doi:10.1080/02331934.2019.1652910

Cited by 6 publications

(8 citation statements)

References 13 publications

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“…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%

“…In 2008, Li [17][18][19] studied the nonlinear ordered variational inequalities and proposed an algorithm to approximate the solution for a class of nonlinear ordered variational inequalities (ordered equations) in real ordered Banach spaces. Very recently, Ahmad et al [20][21][22] considered some classes of ordered variational inclusions involving XOR operator in different settings.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

et al. 2020

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In the setting of real ordered positive Hilbert spaces, a nonlinear fuzzy ordered variational inclusion problem with its corresponding nonlinear fuzzy ordered resolvent equation problem involving XOR operation has been recommended and solved by employing an iterative algorithm. We establish the equivalence between nonlinear fuzzy ordered variational inclusion problem and nonlinear fuzzy ordered resolvent equation problem. The existence and convergence analysis of the solution of nonlinear fuzzy ordered variational inclusion problem involving XOR operation has been substantiated by applying a new resolvent operator method with XOR operation technique. The iterative algorithm and results demonstrated in this article have witnessed a significant improvement in many previously known results of this domain.

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“…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%

Section: Introductionmentioning

confidence: 99%

Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

et al. 2020

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“…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%

“…(i) If F = I, the identity mapping, G, S = 0, M(F (x), G(x)) = M(x) and R, T are the single-valued mappings, and then GSMOVIP (10) becomes an equivalent problem of finding x ∈ H p , for some a ∈ H p and any b ∈ R such thata ∈ P (x) ⊕ τM(x) − bϕ(x, g(x)). (11)Problem(11) was constructed and examined by Ahmad et al[27], using (γ R , λ)-weak-RRD mappings. (ii) If τ = 1 and ϕ(•, •) = 0, then problem (11) coincides with the problem of finding…”

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confidence: 99%

Convergence Analysis of a Three-Step Iterative Algorithm for Generalized Set-Valued Mixed-Ordered Variational Inclusion Problem

et al. 2021

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This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·,·)-compression XOR-αM-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.

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“…On the other hand, ordered variational inequalities (inclusions) are also very important from the application point of view. A suitable amount of work related to generalized variational inequalities (inclusions) in Hilbert spaces as well as in Banach spaces can be found in [11][12][13][14][15][16][17][18][19][20][21]. Let S be a symmetric operator on H and express an operator C s as C s = (S − iI)(S + iI) −1 , then C s is the Cayley transformation of S. Cayley transformation is a mapping between skew-symmetric matrices and special orthogonal metrics.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of Mixed Cayley Inclusion Problem with XOR-Operation

et al. 2020

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In this paper, we consider the parametric mixed Cayley inclusion problem with Exclusive or (XOR)-operation and show its equivalence with the parametric resolvent equation problem with XOR-operation. Since the sensitivity analysis, Cayley operator, inclusion problems, and XOR-operation are all applicable for solving many problems occurring in basic and applied sciences, such as financial modeling, climate models in geography, analyzing “Black Box processes”, computer programming, economics, and engineering, etc., we study the sensitivity analysis of the parametric mixed Cayley inclusion problem with XOR-operation. For this purpose, we use the equivalence of the parametric mixed Cayley inclusion problem with XOR-operation and the parametric resolvent equation problem with XOR-operation, which is an alternative approach to study the sensitivity analysis. In support of some of the concepts used in this paper, an example is provided.

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Convergence analysis and stability of perturbed three-step iterative algorithm for generalized mixed ordered quasi-variational inclusion involving XOR operator

Cited by 6 publications

References 13 publications

Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

Nonlinear ordered variational inclusion problem involving XOR operation with fuzzy mappings

Convergence Analysis of a Three-Step Iterative Algorithm for Generalized Set-Valued Mixed-Ordered Variational Inclusion Problem

Sensitivity Analysis of Mixed Cayley Inclusion Problem with XOR-Operation

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