The goal of this manuscript is to create a new faster iterative algorithm than the previous writing's sober algorithms. In the setting of Banach spaces, this algorithm is used to analyze convergence, stability, and data-dependence results. Basic numerical examples are also provided to highlight the behavior and effectiveness of our approach. Ultimately, the proposed approach is used to solve the functional Volterra-Fredholm integral problem as an application.

This work presents a practical iterative algorithm, extending the inertial Mann iteration, for solving split fixed-point problems with demicontractive mappings in real Hilbert spaces. We rigorously establish both its weak and strong convergence under clearly defined parametric conditions. Our methodology utilizes versatile two-step selection techniques with both fixed and variable step sizes. Compelling numerical experiments confirm the algorithm's accuracy and computational efficiency in approximating solutions to these challenging problems.

A significant advancement in the field of fixed point theory is presented in this manuscript. The existence and uniqueness of strong tripled coincidence points for F-contractive mappings in metric spaces were investigated. An extension of this analysis to multivalued F-contractive mappings was provided, establishing the existence of tripled fixed points within this generalized setting. Existing findings in the literature were generalized and refined by these results, offering a more comprehensive understanding of fixed point phenomena. Furthermore, the practical applicability of these theoretical contributions was demonstrated through the study of solutions to various forms of nonlinear integral equations and integral-type inequalities.

The existence and uniqueness of solutions to fractional-order functional and neutral functional integrodifferential equations with infinite delay and multi-term fractional integral boundary conditions are investigated in this paper. Rigorous mathematical frameworks for analyzing these hybrid equations are established utilizing fixed point theorems. Notably, the fractional derivative is defined in the Liouville-Caputo sense, allowing for a comprehensive examination of nonlocal dynamics. Illustrative examples are provided to complement the theoretical results and demonstrate the applicability and practicality of the main results.

In this corrigendum, we would like to emphasize that the findings in paper ^[1] are a generalization of the results presented by Zhou et al. in ^[2]. This remark highlights key elements of prior research that are relevant to our work ^[1]. This correction does not alter any results or the conclusion of the article.

This manuscript introduces modified $\mathrm{\Re }$-rational contractions for single self-maps, leveraging $\omega$-distance in a relational-theoretic metric space. This novel approach establishes the existence and uniqueness of a fixed point for self-maps, specifically by applying the locally $\mathrm{\Theta }$-transitivity property. We support our theoretical advancements with compelling examples and demonstrate their practical significance by solving a fourth-order boundary value problem related to transverse oscillation in a homogeneous bar and a first-order periodic boundary value problem.

This study explored the theoretical characteristics of a $p$-Laplacian fractional-order differential equation. This equation was subject to both infinite-point boundary value requirements and nonlocal integral value constraints. We began by examining the associated Green's function, deriving its explicit expression and unique properties. These properties were then utilized to establish the existence and uniqueness of positive solutions through the application of the Banach fixed-point technique. Furthermore, we employed the nonlinear alternative of Leray-Schauder type, specifically Guo-Krasnoselskii's fixed-point theorem on cones, to demonstrate existence results for cases where the nonlinearity exhibits singularity with respect to the time variable. The practical relevance and applicability of our findings were illustrated through compelling examples. This research significantly contributed to the field of fractional differential equations, particularly within the domain of $p$-Laplacian Hadamard fractional differential equations.

This paper addresses a class of Hilfer fractional stochastic nonlinear integro-differential equations incorporating impulsive effects and optimal control in Hilbert spaces. We first establish the existence of mild solutions, ensuring the solvability of the system through the application of fractional calculus, stochastic analysis, and fixed-point techniques. The analytical framework effectively manages the combined difficulties arising from nonlocal operators, stochastic perturbations, and impulsive dynamics. Subsequently, we formulate the associated optimal control problem and derive the necessary conditions for optimality. An illustrative example is provided to demonstrate the practicality and robustness of the theoretical results.