Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application

Abstract

The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (\alpha, \beta, \gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.