Mijanur Rahaman

An iterative algorithm for a system of generalized implicit variational inclusions

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.

Generalized vector complementarity problem with fuzzy mappings

In this paper, we introduce and study a generalized vector complementarity problem with fuzzy mappings. Under suitable conditions, we have shown that generalized vector complementarity problem with fuzzy mappings is equivalent to generalized vector variational inequality problem with fuzzy mappings. We derive some existence results for our problem. Results of this paper represent a significant improvement and refinement of the previously known results.

Extended Mixed Vector Equilibrium Problems

We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005), some existence results for both problems are proved in noncompact domain.

The Yosida approximation iterative technique for split monotone Yosida variational inclusions

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.

Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems

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.

Generalized Monotone Mappings with Applications

In this work, we introduce a generalized monotone mapping and we call it H(∙,∙)-cocoercive mapping. Then, we have extended this concept of H(∙,∙)-cocoercive mapping to H(∙,∙)-η-cocoercive mapping. Further, we have proved some of the properties of H(∙,∙)-cocoercive and H(∙,∙)-η-cocoercive mappings and finally apply these concepts to solve some generalized variational inclusions and system of variational inclusions.

Relaxed η-proximal Operator for Solving a Variational-Like Inclusion Problem

AbstractIn this paper, we introduce a new resolvent operator and we call it relaxed η-proximal operator. We demonstrate some of the properties of relaxed η-proximal operator. By applying this concept, we consider and study a variational-like inclusion problem with a nonconvex functional. Based on relaxed η-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.

Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.