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This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, integrating past and present influences with nonlinear interactions. They are widely applied in control theory, population dynamics and physics. These equations are essential for solving complex real-world problems.

Demonstrating the solution’s existence and uniqueness in the equation is accomplished by using the Picard iterative method as a key technique. Using the trapezoidal discretization method is the chosen approach for numerically approximating the solution, yielding a nonlinear system of algebraic equations. The trapezoidal method (TM) exhibits quadratic convergence to the solution, supported by the application of a discrete Grönwall inequality. A novel Grönwall inequality is introduced to demonstrate the convergence of the considered method. This approach enables a detailed analysis of the equation’s behavior and facilitates the development of a robust solution method.

The numerical results conclusively show that the proposed method is highly efficacious in solving NVFHIEs, significantly reducing computational effort. Numerical examples and comparisons underscore the method’s practicality, effectiveness and reliability, confirming its outstanding performance compared to the referenced method.

Unlike existing approaches that rely on a combination of methods to tackle different aspects of the complex problems, especially nonlinear integral equations, the current approach presents a significant single-method solution, providing a comprehensive approach to solving the entire problem. Furthermore, the present work introduces the first numerical approaches for the considered integral equation, which has not been previously explored in the existing literature. To the best of the authors’ knowledge, the work is the first to address this equation, providing a foundational contribution for future research and applications. This innovative strategy not only simplifies the computational process but also offers a more comprehensive understanding of the problem’s dynamics.

The purpose of this study is to provide a review of the existing research landscape on work-life balance and women’s career motivation. It examines the relationship between work-life balance and career motivation in the context of Indian women. Specifically, it explores how the work-life balance of women influences the motivational aspects of their careers.

The research uses a systematic literature review to identify and analyze relevant literature on work-life balance and women’s career motivation among Indian women from the Scopus database.

The study uncovers critical insights into the connection between work-life balance and women’s career decisions. It gives insight on how work-life balance significantly impacts women’s career choices. The SLR reveals a notable and consistent upward trend in the domains of work-life balance and career motivation among women.

The findings of this study can inform organizations in tailoring policies that foster women’s career growth while simultaneously supporting a healthy work-life balance. In addition, the research can empower women to make informed decisions about their careers and personal lives. Ultimately, it contributes to creating a more inclusive and gender-equitable work environment, promoting both women’s career aspirations and their overall well-being.

This research stands out in its examination of the relationship between work-life balance and women’s career motivation, particularly in the unique context of Indian women. While previous studies have explored these topics individually, this research bridges the gap by investigating their interplay. Moreover, the application of a systematic literature review approach to these variables in the context of Indian women represents a novel contribution.