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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 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]

This work is concentrated on the study of a system of mixed generalized Cayley variational inclusions. Parallel Mann iteration process is defined in order to achieve the solution. We define an altering point problem which is equivalent to our system and then we construct general parallel S -iteration process. Finally, we discuss convergence criteria and provide an example. [ABSTRACT FROM AUTHOR]

In this paper, we consider and study a system of generalized variational inclusions involving Cayley operators and an XOR-operation in q-uniformly smooth Banach spaces. To obtain the solution of the system of generalized variational inclusions involving Cayley operators and an XOR-operation, we use some properties of Cayley operators as well as an XOR-operation. We also discuss the convergence criterion. In support of our main result, we provide an example. [ABSTRACT FROM AUTHOR]

A new inclusion problem is introduced using generalized Cayley operator and we call it Cayley inclusion problem. We also study its corresponding resolvent equation problem. By using a generalized resolvent operator and generalized Yosida approximation operator, first we establish a fixed point formulation for Cayley inclusion problem. An algorithm is defined to find the solution of Cayley inclusion problem. An existence and convergence result is proved. Secondly, we have shown the equivalence of Cayley inclusion problem with a resolvent equation. We define an iterative algorithm with some of its equivalent forms for solving resolvent equation problem. A numerical example is constructed and a convergence graph is shown by using MATLAB program. [ABSTRACT FROM AUTHOR]

In this paper, we first study a composite relaxed resolvent operator and prove some of its properties. After that, we introduce a Yosida approximation operator based on the composite relaxed resolvent operator and demonstrate some properties of the Yosida approximation operator. Finally, we obtain the solution of a system of Yosida inclusions by applying these concepts. We construct a conjoin example in support of many concepts derived in this paper. Our concepts and results are new in the literature and can be used for further research. [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]

In this paper, we study the weak and strong versions of generalized composite vector equilibrium problem in Hausdorff topological vector spaces. The generalized KKM-theorem due to [3] is applied to solve both the problems in non-compact setting. Some special cases are listed and examples are constructed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a system of generalized implicit variational inclusions which consists of three variational inclusions. We design an iterative algorithm with error terms based on relaxed resolvent operator due to Ahmad et al. (Stat Optim Inf Comput 4:183-193, 2016) for approximating the solution of our system. The convergence of the iterative sequences generated by the iterative algorithm is also discussed. An example is given which satisfy all the conditions of our main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new resolvent operator and we call it relaxedη-proximal operator. We demonstrate some of the properties of relaxedη-proximal operator. By applying this concept, we consider and study a variational-like inclusion problem with a nonconvex functional. Based on relaxedη-proximal operator, we define an iterative algorithm to approximate the solutions of a variational-like inclusion problem and the convergence of the iterative sequences generated by the algorithm is also discussed. Our results can be treated as refinement of many previously known results. An example is constructed in support of Theorem 1. [ABSTRACT FROM AUTHOR]

This article deals with the study of a variational-like inequality problem which involves the generalized Cayley operator. We compare our problem with a fixed point equation, and based on it we construct an iterative algorithm to obtain the solution of our problem. Convergence analysis as well as stability analysis are studied. [ABSTRACT FROM AUTHOR]

In this paper, we consider and study a system of multi-valued mixed variational inclusions with XOR-operation ⊕ in real ordered uniformly smooth Banach spaces. This system consists of bimappings, multi-valued mappings and Cayley operators. An iterative algorithm is suggested to find the solution to a system of multi-valued mixed variational inclusions with XOR-operation ⊕ and consequently an existence and convergence result is proved. In support of our main result, an example is constructed. [ABSTRACT FROM AUTHOR]