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, Volterra q-integral equations are solved by using the method of q-differential transformation. Exact solutions of linear and nonlinear q-integral equations have been investigated. To illustrate the method, several problems are discussed for the effectiveness and performance of the proposed method.

In this work, a co-variational inequality problem and a co-resolvent equation problem are introduced and investigated. It is shown that the fixed point problem is equivalent to the problem of co-variational inequality. The co-variational inequality problem and the co-resolvent equation problem are equivalent due to this resemblance. The coresolvent equation problem is solved using an iterative approach that we provide at the final stage. Our findings may be seen as an enhancement of several established findings.

In this article, a nonlinear system of generalized ordered XOR-inclusion problems in Hilbert space is introduced and studied. Initially, we define the resolvent operator related to the $(\alpha ,\lambda )$-XOR-weak-ANODD multivalued mapping. Using the fixed point technique, we demonstrate the results of existence. In order to make the suggested system more realistic, we create the S-iterative algorithm and demonstrate that the sequence generated through this technique strongly converges with the proposed system’s solution. One example is provided in support of the existence result as well.

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.