Aftab Hussain

In this paper, we introduce a new class of generalized contractions, called enriched (Ψ, φ )‐contractions. Within this framework, we establish several fixed‐point theorems together with corresponding convergence results, which extend and unify a range of existing results in the literature. To demonstrate the applicability of the proposed approach, we provide illustrative examples and show that the obtained fixed‐point and convergence results ensure the existence of solutions for certain classes of integral equations. These findings broaden the theoretical scope of contraction mappings and highlight their usefulness in the analysis of integral equations.

In the realm of signal processing, the Hilbert transform and quadratic phase Fourier transform (QPFT) are well-established tools for analyzing complex-valued signals. However, their efficiency to analyze the quaternionic-valued signals is almost negligible due to the higher-dimensional nature of such signals. In this study, we explored this area by introducing a novel integral transform, namely, the quadratic-phase Hilbert transform in the realm of quaternion domains (briefly referred to as the quaternion quadratic-phase Hilbert transform (Q-QPHT)), by combining the merits of the Hilbert transform and QPFT. The study began with a comprehensive investigation of the fundamental properties of the proposed transform including the derivation of Parseval's formula and a detailed characterization of its range. Subsequently, general relationships, illustrative examples, and Hausdorff-Young inequalities associated with the proposed Q-QPHT were established. These findings shed light on the broader applications of the Q-QPHT in signal processing; particularly in handling complex quaternionic-valued signals that require simultaneous control over multiple aspects. Finally, the validation of the obtained results was established by well-constructed examples and numerical simulations.

This paper introduces the generalized fuzzy contraction in k-fuzzy metric spaces, a novel extension of the classical Meir-Keeler contraction principle. The main discovery is that several fixed point theorems, previously limited to classical or fuzzy metric spaces, remain valid under more general k-fuzzy conditions. This breakthrough broadens the applicability of fixed point theory to systems with multi-parameter uncertainty and non-uniform convergence, thereby offering a new mathematical tool for analyzing complex real-world problems in control theory, optimization, and data science.

This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to have strong convergence to approximate the fixed point.

This paper presents novel fixed point (FP) theorems for a specific class of multivalued contractions, referred to as ”almost Fisher type multivalued F-contractions” within complete metric spaces (MSs) endowed with a Γ-transitive binary relation ℜ. These theorems establish the existence of FPs for such contractions and explore their intrinsic properties. Illustrative Examples are provided to demonstrate the applicability and effectiveness of the proposed results. An application for solving second-order differential inclusions (SODIs) is provided under these contractives.

Purpose: This study proposes a framework for third-party logistics service providers (3PLs) in emerging economies. This framework examines the landscape of its enablers to facilitate smart warehouse adoption. Design/methodology/approach: Based on an extensive literature search, this study presents a novel three-phase framework that identifies 9 enablers and 36 sub-enablers under the Technology–Organization–Environment (TOE) framework through expert judgments. This study employs an Analytical Hierarchy Process (AHP) to evaluate these enablers. Furthermore, the robustness of the enabler ranking is assessed through a sensitivity analysis. Findings: Findings based on the TOE framework highlight the significance of technology type in determining its acceptance by 3PLs. Moreover, the study reveals that market orientation and infrastructure, supported by the supply chain network, can be significant enablers of 3PLs in smart warehousing. Additionally, addressing the social environment of warehousing and adopting effective cost-management strategies can further enhance the effectiveness of smart warehousing for 3PLs in the future. Research limitations/implications: The framework proposed in this study is specifically tailored for emerging economies and may not directly apply to developed economies. It is crucial to note that while the enablers were identified through a comprehensive literature review and expert validation, there is a possibility that certain enablers may have been overlooked, which could be a potential area for future research. Originality/value: To the best of the authors’ knowledge, this study is among the first to examine 3PL providers from a smart warehouse perspective under the TOE framework. This research aims to assist decision-makers in comprehending the challenges and opportunities within various sub-enablers of TOE contexts.

This paper establishes new fixed‐point (FP) theorems for Suzuki–Rational ( ψ , ϕ )‐type multivalued contractions in complete rectangular M ‐metric spaces (RM‐MSs). These theorems ensure the existence of fixed points and provide significant insights into the structural properties of such contractions. Furthermore, we derive important results concerning contractions defined on closed balls within RM‐MS. To demonstrate the originality and applicability of our findings, we present illustrative examples that validate the effectiveness of the proposed theorems. Finally, we investigate the solvability of a system of nonlinear matrix equations (NMEs) in the framework of our study. This application highlights the practical relevance of the theoretical developments and their potential for solving real‐world problems.

This paper explores the significance and implications of common γ ‐fuzzy fixed point results related to γ ‐fuzzy contraction as a novel form of contraction in complete b ‐metric space. Theoretical developments and theorems provide a solid foundation for understanding utilization of the properties of γ ‐fuzzy contraction, showcasing its efficiency through numerous examples and establishing stability and convergence properties. Moreover, some conventional fixed point results are incorporated as the direct consequences of our main findings.