Interpolative metric spaces were recently introduced by Karapinar et al., who established fixed point theorems in this framework. In this paper, we clarify their position within the hierarchy of generalized metric spaces by proving that every interpolative metric is, in fact, a bmetric. Building on this structural clarification, we investigate nonlinear contractions in the setting of bsuprametric spaces, a class that strictly generalizes bmetric spaces and naturally accommodates quadratic terms in the triangletype inequality. We establish a Matkowskitype fixed point theorem for generalized contractions of iri type in bsuprametric spaces. Our approach replaces the classical linear contraction coefficient with a control function θ ∈ Θ1, thereby strengthening the contraction framework while balancing this generality with the natural assumption that Picard orbits are bounded. This yields existence and uniqueness of fixed points and convergence of Picard iterates under conditions that extend beyond traditional Lipschitztype bounds. As corollaries, we recover weaker versions of several wellknown fixed point theorems, including results of Czerwik and Berzig, demonstrating that our framework unifies and generalizes earlier principles. For applications of interpolative contractions to integral and differential equations, we refer the reader to recent works in the literature, while emphasizing that the present paper is primarily structural and foundational. Overall, this work broadens the scope of fixed point theory in generalized metric spaces and highlights the structural role of boundedness in nonlinear contraction analysis.
This study aims to assess the stability of time-delayed variable fractional-order difference systems (Fvods). The study introduces new criteria for evaluating the stability of these modern types of systems. These criteria are derived by transforming the target system into its equivalent forms of Volterra systems of the convolution type. This research utilizes specific properties of the Z-transform method to formulate the required criteria. The accuracy of these results is confirmed through numerical verification using examples related to the stability of solutions within these systems.
This study investigates a novel class of boundary value problems governed by Caputo conformable fractional differential pantograph equations, characterized by a proportional delay of the form phi(gamma t), with 0 < gamma < 1. Such models effectively describe phenomena in physics, engineering, and biological systems that exhibit both memory effects and self-similar dynamics. We formulate a general nonlinear problem and establish the existence and uniqueness of solutions through fixed-point techniques, including Banachs contraction principle and Schauders fixed-point theorem, under appropriate assumptions on the nonlinear term Phi (x, phi(t), phi(gamma t)). Furthermore, the Ulam-Hyers stability of the proposed problem is analyzed, offering insights into the robustness of solutions with respect to perturbations in the initial data.
This article focuses on the study of fixed point theorems for PRESICS type contractive mappings within the framework of "soft metric spaces", particularly when the underlying parameter set is finite. By extending classical contraction principles, we establish rigorous existence and uniqueness results that broaden the current theory of soft metric spaces. The necessity of the imposed conditions is illustrated through carefully designed examples, demonstrating that these assumptions cannot, in general, be relaxed. In addition, explanatory remarks are included to clarify the scope and relevance of the results in relation to existing fixed point theorems. Furthermore, we explore potential applications in nonlinear analysis, showing how the developed theoretical framework can guarantee the existence, uniqueness, and iterative convergence of solutions to nonlinear problems under uncertainty. These findings not only generalize known results to a wider setting but also provide a foundation for future research and practical applications in mathematics and applied sciences.
The primary objective of this research work is to establish strong coupled fixed point results in multiplicative metric spaces using maximum and product types of cyclic coupled contractions. In support of our main results, we present trivial and nontrivial illustrative examples within the space. Furthermore, an application of the Lebesgue integral equation is provided in aid of the proposed work on multiplicative metric spaces. It has the potential to be extended in many directions in the context of different types of metric spaces, with different types of contractive conditions for nonlinear mappings, and with the application of different types of integral equations.
