Annals of Communications in Mathematics

AbstractIn this work, we investigate the existence of solutions for Hadamard fractional differential equations with integral boundary conditions in a Banach space. We will make use the measure of noncompactness and the Monch fixed point theorem to prove the ¨ main results. An example is given to illustrate our results.

AbstractIn this work, we investigate the Hyers-Ulam stability by using direct and fixed point methods for the quartic functional equation for positive integer p ≥ 3.

AbstractIn this paper, we investigate some stability results of the following finite dimensional additive functional equation where n is the positive integer with N − {0, 1, 2} and k is the only odd positive integers, in Fuzzy Normed space using direct and fixed point approaches.

AbstractIn this work, we investigate the generalized Ulam-Hyers stability of the ωdimensional cubic functional equation where ω ≥ 4, in Banach spaces using direct and fixed point methods.

ABSTRACT.In this paper, we determine some stability results concerning the quartic functional equation as of the form\[\sum_{b=1}^{s} \phi\!\left(-v_b + \sum_{a=1,\,a\ne b}^{s} v_a\right)- 4 \sum_{1 \le a < b < c \le s} \phi(v_a + v_b + v_c)- \sum_{b=1}^{s} \phi(2v_b)\]\[= (-4s+14)\sum_{a=1,\,a\ne b}^{s} \phi(v_a + v_b)+ (s-8)\phi\!\left(\sum_{a=1}^{s} v_a\right)\]\[\quad + 2 \left[\sum_{a=1,\,a\ne b}^{s} \phi(v_a - v_b)+ (s^{2}-7s+7)\sum_{a=1}^{s} \phi(v_a)\right],\]where any positive integers \( s \ge 3 \), in Banach algebra via direct and fixed point approaches.

AbstractIn this work, authors investigate the generalized Hyers-Ulam stability of the 4-variable quadratic functional equation of the form

AbstractWe examine the Ulam-Hyers stability of finite variable additive functional equation in fuzzy normed space using classical methods.

AbstractThis paper deals with some existence and uniqueness of random solutions for a coupled system of Caputo–Hadamard fractional differential equations with four-point boundary conditions and random effects in generalized Banach spaces. Some applications are made of generalizations of classical random fixed point theorems on generalized Banach spaces. An illustrative example is presented in the last section.

AbstractIn this paper, using the idea of a coincidence point for nonlinear mappings in any number of variables, we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of generalized intuitionistic fuzzy metric spaces. Recently, many authors have conducted in-depth research on coupling, triple and quadruple fixed point theorems in the context of partially ordered complete metric spaces with different contractive conditions. In partially ordered generalized intuitionistic fuzzy metric spaces, we demonstrate several theorems regarding multidimensional co-incidence points and common fixed points for ϕ -compatible systems.

Abstract: In this paper we introduce a new orbit-based contractive framework in the setting of \( G \)-metric spaces, called \( (m,\alpha) \) \( G \)-path-averaged (\( G \)-PA) contractions with \( m \geq 2 \). This notion extends Fabião’s path-averaged contractions to the triadic geometry of Mustafa–Sims \( G \)-metrics and is designed to avoid collapse to pointwise contractivity. For a \( G \)-continuous self-map on a complete \( G \)-metric space, we establish existence and uniqueness of a fixed point and prove that the Picard iteration converges to it in the sense of \( G \)-convergence. Moreover, we derive explicit quantitative estimates, including a posteriori and a priori geometric error bounds for the iterates. We also relate the new class to the induced metric \( d_G \), showing that every \( G \)-PA contraction yields a path-averaged contraction on \( (X, d_G) \), and we provide examples demonstrating that the \( G \)-PA class can be strictly larger than the Banach-type contraction class. Finally, we obtain multi-step (\( t \)-point) fixed point and convergence results by embedding the recursion into a shift map on the product space \( (X^t, \sigma^t) \) and applying the single-valued theory.