An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing.

This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications.

The equivalence between the ( S , T ) - stabilities of Jungck-type iterative schemes.

In this paper, the stability of Jungck-Multistep iterative scheme is established and the equivalence between the ( S , T ) - stabilities of Jungck-Mann and Jungck-multistep iterative schemes are proved in a normed linear space settings, and a consequence is the equivalence between the ( S , T ) - stabilities of Jungck-Ishikawa and Jungck-Noor iterative schemes.

On random fixed point theorems with applications to integral equations.

This particular research establishes some random fixed point theorems for general nonlinear random contractive operators in the context of partially ordered separable metric spaces. The existence and uniqueness of the random solution for the nonlinear integral equation is obtained by applying the result of the random fixed point. The results generalize and improve on some related works in the literature.•Our theorems are proved in the context of metric space while Saluja and Tripathi [8] proved in the context of partial metric spaces.•Nieto, Ouahab and. Rodriguez-Lopez [9] proved their theorem using Banach contraction mappings while we proved our theorems using Hardy and Rogers contraction mappings.•Rashwan and Albaqeri [3] proved the solution of the random integral equation using the Banach contraction operator while we proved our solution to the random integral equations employing more general contractive operator.