This paper is concerned with a class of singular multi-point boundary value problems (BVPs) subject to integral Riemann–Stieltjes boundary conditions, involving the $\varpi$-Caputo fractional derivative and a nonlinear $p$-Laplacian operator. The analysis is performed in the range $1<p\le 2$. To support the theoretical framework, suitable estimates for the Green's functions arising in the integral formulation of the problem are derived. The existence of at least one solution is further obtained through the application of Schaefer's fixed-point (FP) theorem. The uniqueness of solutions to the associated nonlinear $\varpi$-Caputo fractional differential equation is established by means of the Banach contraction principle. In addition, the stability of solutions is investigated in the sense of both Ulam–Hyers and Ulam–Hyers–Rassias. As a result, the study provides a comprehensive treatment of the existence, uniqueness, and stability properties for the considered singular multi-point fractional BVP with integral Riemann–Stieltjes conditions. The theoretical results are complemented by two examples that illustrate the applicability of the developed framework.

We explored the $AA$-iterative algorithm within the hyperbolic spaces (HSs), aiming to unveil a stability outcome for contraction maps and convergence outcomes for generalized $(\alpha ,\beta )$-nonexpansive ( $G\alpha \beta N$) maps in such spaces. Through this algorithm, we derived compelling outcomes for both strong and $\mathrm{\Delta }$-convergence and weak $w^2$-stability. Furthermore, we provided an illustrative example of $G\alpha \beta N$ maps and conducted a comparative analysis of convergence rates against alternative iterative methods. Additionally, we demonstrated the practical relevance of our findings by applying them to solve the linear Fredholm integral equations (FIEs) and nonlinear Fredholm-Hammerstein integral equations (FHIEs) on time scales.

This paper investigates the existence and uniqueness of solutions for a class of nonlinear $\mathrm{\Omega }$-Caputo fractional differential equations (CFDEs) supplemented with infinite-point boundary conditions. By constructing an appropriate operator framework and employing fixed-point (fp) theorems, including the Banach, the Schaefer, and the Schauder–Tychonoff fp theorems, we establish the existence and uniqueness criteria for the proposed boundary value problem (BVP). The analysis is conducted within suitable Banach spaces, taking into account the properties of the $\mathrm{\Omega }$-Caputo fractional derivative and the nonlocal nature of the boundary conditions. To substantiate the theoretical findings, a concrete example is presented to illustrate the applicability and effectiveness of the main results.

In this paper, using the Schauder and the Banach fixed point (FP) theorems, we examine the existence and uniqueness of solutions in the Banach space $C([0,1])$ for a boundary value problem (BVP) of non-linear third-order $q$-difference equations with the $q$-integral boundary condition. Then, we impose the sufficient condition that allows us to deduce a nonexistence result. Furthermore, we offer some examples to support our main outcomes.

Regarded as a cornerstone of mathematics, the fixed-point (fp) explores invariant outcomes under defined operators, thus offering powerful tools for problems that arise in mathematics, physics, engineering, computer science, and economics. This paper presents a novel iterative method to approximate the fps of non-expansive maps in Banach spaces (BSs). We investigate the stability of the proposed method and provide its convergence analysis. A numerical example further illustrates its performance in comparison to existing iterations. Consequently, we theoretically and numerically prove that our new iterative algorithm converges faster than some leading iterative algorithms in the literature for non-expansive maps. Hence, our results generalize and improve several well-known results in the existing literature.