We introduce the notion of quasi--metric space. After defining the basic topological properties of quasi--metric space, we investigate fixed point of certain mapping in the frame of complete quasi--metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi--metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature. We introduce the notion of quasi--metric space. After defining the basic topological properties of quasi--metric space, we investigate fixed point of certain mapping in the frame of complete quasi--metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi--metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature.

A lot of work has been completed in efforts to extend the notions of soft set and fuzzy soft set and their applications to other domains. However, neither of the two concepts has been examined in the study of functional equations in b-metric spaces. Given this background information, this paper proposes the idea of b-hybrid fuzzy soft contraction in b-metric space and investigates new criteria for the existence of fixed points for such mappings. The significance of the obtained principal result lies in the fact that the contractive inequalities can be specialized in various ways, depending on the choice of the parameters, thereby making it possible to unify, deduce, and refine several corresponding results. To motivate further studies in the directions studied herein, two applications regarding decision-making problems and an existence theorem of integral inclusion are considered, using fuzzy soft set-valued maps.

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and $\mathcal{Z}$Z -contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades.

This study uses important findings from Hilbert Space (HS) theory to suggest new fixed-point theorems for Three Self-Mappings (3-SMs) that apply to Generalized Inner Product Spaces (GIPS). We made it apparent when Common Fixed Points (CFPs) can exist and be unique, even when the contraction criteria aren’t as strict. This improvement makes the theory better for systems with more than one operator. Our results are important in two main areas: (1) Artificial Intelligence (AI), where we use fixed-point analysis to make sure that Deep Equilibrium Models (DEMs) will work correctly, and (2) Cryptography (Crypto), where we use the mathematical properties of inner product spaces to make new lattice-based designs for Post-Quantum Protocols (PQPs). Real-world examples from nonlinear analysis and computational proof of the presented theorems support the theoretical contributions. This work combines advanced functional analysis with modern problems in Machine Learning (ML) and cybersecurity, giving it both mathematical depth and real-world usefulness.

In this work, a family of hybrid contractions, termed Jaggi-type hybrid (ℵ-τ)-contractive mapping is proposed in metric space equipped with a graph and new conditions under which the mapping is a Picard operator are studied. The novel ideas proposed in this manuscript are exemplified to display the validity of the presented results and to show how they differ from the existing ones. Additionally, some corollaries which reduce our proposed notion to some recently announced concepts in the existing findings are indicated and examined. Finally, we study Ulam-type stability for the fixed point equations with hybrid contractions.

The aim of this work is to investigate the concept of a new hybrid Suzuki contractive by using the Rus-Reich-Ćirić-type interpolative mappings in -metric spaces. We seek the presence and uniqueness of a fixed point of such new contraction type mappings and prove some related results. We further give an application of Ulam-Hyers-type stability to show the well-posedness of our results.