Rais Ahmad

This paper presents two inertial viscosity Mann-type extrapolated algorithms for finding a common solution to the variational inequality problem involving a monotone and Lipschitz continuous operator and the fixed-point problem for a demicontractive mapping in real Hilbert spaces. The proposed algorithms feature an adaptive step size strategy, computed iteratively, which circumvents the need for prior knowledge of the operator’s Lipschitz constant. Under appropriate assumptions, we establish two strong convergence theorems guaranteeing the robustness of the methods. Furthermore, we provide a comparative performance analysis of the proposed algorithms against some existing strongly convergent schemes, supported by numerical experiments with MATLAB-based graphical illustrations.

The aim of this work is to study a system of variational inclusions involving generalized Yosida and Cayley operators through inertial extrapolation scheme in real Banach space. To obtain faster convergence of the sequences generated by algorithm, we use one inertial extrapolation scheme, although we have established some more iterative schemes. To achieve our goal, we prove an important Lemma ensuring the convergence of sum of two sequences. We provide a numerical example.

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.

In this article, we study a generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation. It is shown that the generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation is equivalent to a fixed point equation. We have proved that the generalized Yosida approximation operator is Lipschitz continuous. Finally, we prove an existence and convergence result for our problem.

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.

In this paper, we study a co-variational inequality problem involving Yosida approximation operators in real uniformly smooth Banach space and define an iterative method to obtain its solution. We prove some properties of Yosida approximation operator for our purpose, that is strongly accretivity and Lipschitz continuity. An existence as well as convergence result is proved for co-variational inequality problem involving Yosida approximation operators using the concept of nonexpansive sunny retraction.

In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real Banach space and for the Yosida resolvent equation problem in q-uniformly smooth Banach space. For faster convergence, we apply an inertial extrapolation scheme for both the problems. An example is provided.

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.

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.

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.