Cayley inclusion problem with its corresponding generalized resolvent equation problem in uniformly smooth Banach spaces

In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that our system admits a unique solution by using the properties of q-uniformly smooth Banach space, and we discuss the convergence criteria for sequences generated by iterative algorithm. Two examples are constructed, and an application is provided.

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“…The novelty of work lies in the fact that our results are refinement of previously known results (see for example [8,9,13,18,26,28,33,36]).…”

Section: Discussionsupporting

confidence: 81%

Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space

et al. 2022

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“…The class of operators considered in this paper can be further exploited for other classes of varional inclusions problems under different setings. The techniques presented in this paper can be further exploited to study various classes of problems via Cayley operators, see for example [1,2,3,4,5,6,7,8,9,10,12,14,15,16,17,19,20,22,23,25,27,28,29,30,31,33,34,35].…”

Section: Discussionmentioning

confidence: 99%

“…(1) By taking F ≡ 0 and A-monotonicity of the set-valued mapping M instead of H(•, •)-monotonicity, GCVIP (6) reduces to the problem of finding x ∈ X such that 0 ∈ C A M,λ (x) + M (x). This problem was considered and studied by Rais et al [28] in the setting of uniformly smooth Banach spaces.…”

Section: H(••)mentioning

confidence: 99%

Krasnoselskii-Type Approximation Solvability of a Generalized Cayley Inclusion Problem in Semi-Inner Product Space Mohd Iqbal Bhat, Mudasir A. Malik and Bisma Zahoor

2022

Electronic Journal of Mathematical Analysis and Applications

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In this paper, we introduce and study a generalized Yosida approximation operator and generalized Cayley operator associated to H(•, •)monotone operator and discuss some of their properties in semi-inner product spaces. An example is constructed in support of the various results proved. As an application we consider a generalized Cayley inclusion problem in semi-inner product spaces which is more general than the variational inclusion problem. Using the generalized resolvent operator, generalized Yosida approximation operator and generalized Cayley operator we develop an iterative algorithm to approximate the solution of generalized Cayley inclusion problem. Furthermore, an existence and convergence result is proved.

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“…Problem (10) was investigated and studied by Ahmad et al [26], and the results were published in Applicable Analysis.…”

Section: Problem Formulationmentioning

confidence: 99%

Three-Step Iterative Algorithm for the Extended Cayley–Yosida Inclusion Problem in 2-Uniformly Smooth Banach Spaces: Convergence and Stability Analysis

Ali,

Wang,

Ahmad

2024

Mathematics

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In this article, we investigate and study an extended Cayley–Yosida inclusion problem. We show that our problem is equivalent to a fixed-point equation. Based on the fixed-point equation, we develop a three-step iterative algorithm to solve our problem. Finally, we illustrate the convergence of the proposed algorithm with an example, computational table, and convergence graph by using MATLAB 2018b.

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Cayley inclusion problem with its corresponding generalized resolvent equation problem in uniformly smooth Banach spaces

Cited by 9 publications

References 13 publications

Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space

Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space

Krasnoselskii-Type Approximation Solvability of a Generalized Cayley Inclusion Problem in Semi-Inner Product Space Mohd Iqbal Bhat, Mudasir A. Malik and Bisma Zahoor

Three-Step Iterative Algorithm for the Extended Cayley–Yosida Inclusion Problem in 2-Uniformly Smooth Banach Spaces: Convergence and Stability Analysis

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