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In this article, we introduce a new kind of split monotone variational inclusion problem involving Cayley operator in the setting of infinite-dimensional Hilbert spaces. We develop a general iterative method to approximate the solution of the split monotone variational inclusion problem involving Cayley operator. Under some suitable conditions, a convergence theorem for the sequences generated by the proposed iterative scheme is established, which also solves certain variational inequality problems related to strongly positive linear operators. Finally, a numerical example is presented to study the efficiency of the proposed algorithm through MATLAB programming. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new type of split monotone Yosida inclusion problem in the setting of infinite-dimensional Hilbert spaces. To calculate the approximate solutions of split monotone Yosida inclusion problem, first we develop a new iterative algorithm and then study the weak as well strong convergence analysis of iterative sequences generated by the proposed iterative algorithm by using demicontractive property, nonexpansive property, and strongly positive bounded linear property of mappings. A numerical example is formulated to explain our main result through MATLAB programming. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized variational inclusion problem involving difference of monotone operators in Hilbert spaces. We established equivalence between the generalized variational inclusion problem and a fixed point problem. We establish an Ishikawa type iterative algorithm for solving a generalized variational inclusion problem involving difference of monotone operators, which is more general than Mann-type iterative algorithm. An existence result as well as a convergence result are proved separately. The problem of this paper is more general than many existing problems in the literature. Several special cases of generalized variational inclusion problem involving difference of monotone operators are also mentioned. [ABSTRACT FROM AUTHOR]

We focus our study on a co-variational inequality problem involving two generalized Yosida approximation operators in real uniformly smooth Banach space. We show some characteristics of a generalized Yosida approximation operator, which are used in our main proof. We apply the concept of nonexpansive sunny retraction to obtain a solution to our problem. Convergence analysis is also discussed. [ABSTRACT FROM AUTHOR]

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field. [ABSTRACT FROM AUTHOR]