The design of the techniques and algorithms used by the static, dynamic and interactive security testing tools differ. Therefore, each tool detects to a greater or lesser extent each type of vulnerability for which they are designed for. In addition, their different designs mean that they have different percentages of false positives. In order to take advantage of the possible synergies that different analysis tools types may have, this paper combines several static, dynamic and interactive analysis security testing tools—static white box security analysis (SAST), dynamic black box security analysis (DAST) and interactive white box security analysis (IAST), respectively. The aim is to investigate how to improve the effectiveness of security vulnerability detection while reducing the number of false positives. Specifically, two static, two dynamic and two interactive security analysis tools will be combined to study their behavior using a specific benchmark for OWASP Top Ten security vulnerabilities and taking into account various scenarios of different criticality in terms of the applications analyzed. Finally, this study analyzes and discuss the values of the selected metrics applied to the results for each n-tools combination.

In this article, we propose a new methodology to construct and study generalized three-step numerical methods for solving nonlinear equations in Banach spaces. These methods are very general and include other methods already in the literature as special cases. The convergence analysis of the specialized methods is been given by assuming the existence of high-order derivatives which are not shown in these methods. Therefore, these constraints limit the applicability of the methods to equations involving operators that are sufficiently many times differentiable although the methods may converge. Moreover, the convergence is shown under a different set of conditions. Motivated by the optimization considerations and the above concerns, we present a unified convergence analysis for the generalized numerical methods relying on conditions involving only the operators appearing in the method. This is the novelty of the article. Special cases and examples are presented to conclude this article.

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The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case. A process is developed based on majorizing sequences and the notion of restricted Lipschitz condition to provide a semi-local convergence analysis for the third convergent order Noor–Waseem method. Due to the generality of our technique, it can be used on other high order methods. The convergence analysis is enhanced. Numerical applications complete are used to test the convergence criteria.

The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the given iterative method was carried out while assuming the existence of certain higher-order derivatives. In contrast to this approach, the convergence analysis is carried out in the present study by considering the hypothesis only on the first-order Fréchet derivatives. This study further provides an estimate of convergence radius and bounds of the error for the considered method. Such estimates were not provided in earlier studies. In view of this, the applicability of the given method clearly seems to be extended over the wider class of functions or problems. Moreover, the numerical applications are presented to verify the theoretical deductions.

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A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results.

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