We introduce a new explicit composite iteration scheme with a viscosity iteration method for approximating a common fixed point of Lipschitzian semigroup on a compact convex subset of a smooth Banach space. We show that the Iterative sequence converges strongly to a common fixed point under some parameter controlling conditions. Our results extend and improve the recent results by Saeidi.

We construct one− step Iterative process for an  − nonexpan-sive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study 4− convergence and strong convergence of the Iterative process to the common fixed point of the mappings. Our results are new and valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

In this paper, we study Projected non-stationary Simultaneous It-erative Reconstruction Techniques (P-SIRT). Based on algorithmic op-erators, convergence result are adjusted with Opial’ s Theorem. The advantages of P-SIRT are demonstrated on examples taken from to-mographic imaging.

There exist many sixth-order Iterative methods for solving nonlinear scalar equations. The purpose of this work is to bring them together. We develop a scheme for unifying sixth-order Iterative methods. Convergence analysis shows that the methods and family of methods, formulated through the scheme are sixth-order convergent. Finally, some computational results are reported to verify the developed theory.

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications that work with multiple signals maintaining some degree of dependency, e. g., radar and sensor networks. We introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion of the convergence of our method, called Simultaneous Iterative Method (SIM). In this study, we compared our method with other group-sparse reconstruction techniques, namely Simultaneous Orthogonal Matching Pursuit (SOMP) and Block Iterative Method with Adaptive Thresholding (BIMAT), through numerical experiments. The simulation results demonstrated that SIM outperformed these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIM is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.