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This study is motivated through the interesting non-Arcchimedean stability results of ρ-inequalities and ρ-equations arising from linear, second power, third power and fourth power mappings. The aim of this paper is to determine the solutions of new multiplicative inverse µ-inequalities and µ-equations arising from multiplicative inverse mapping. Further, their stabilities involved with various superior limits are proved in the context of non-Archimedean complete normed spaces.

The advantage of various fuzzy normed spaces is to analyse impreciseness and ambiguity that arise in modelling problems. In this paper, various classical stabilities of a new hexic functional equation in di erent fuzzy spaces like fuzzy Banach space, Felbin’s fuzzy Banach space and intuitionistic fuzzy Banach space are presented, concerning the Ulam’s theory of stabilities of equations. To validate the stability results, experimental results are presented. Also, a comparative study of the results obtained in this investigation are provided.

The aim of this paper is to study the asymptotic convergence of the sequences. Concretely, we will give the asymptotically statistical convergence of sequences. The asymptotically statistical convergence is studied in many papers including papers [3], [5], [23], [26], [29], [39], [41]. In this paper, we introduce and investigate the concepts of asymptotically deferred statistical equivalent functions of order $ \alpha $ and strong asymptotically deferred statistical equivalent functions of order $ \alpha $ defined on discrete countable amenable semigroups, which generalizes some of the results known in the literature. This is achieved by introducing the Folner sequences and sequences of non-negative integers. Based on this concept we apply it to the approximation theory, and we have proved the Korovkin type theorem and study the rate of convergence for positive linear operators which are deferred statistically convergent of order $ \alpha $. [ABSTRACT FROM AUTHOR]

In real-world inventory problems, the deterioration rate is usually treated as an uncontrolled factor. However, by adopting certain preservation techniques, such deterioration rate can be controlled up to a desired level. Moreover, in certain business affairs, the supplier also provides a permissible delay in payment to encourage the vendors to have further sales. In this paper, we develop an inventory model that considers the power pattern demand under trade credit, permissible completely backlogged shortages, and suitable investment in preservation technology. Additionally, to make the model more realistic, we apply the learning effect to the holding costs. We develop the mathematical model of the problem and its solving policy in both crisp and fuzzy environments. The main purpose of the model is to obtain the optimum preservation technology-based cost and cycle time that maximize the overall profit. Furthermore, to validate our findings, we consider numerical examples and subsequently demonstrate the concavity of the profit function via Mathematica 11.1.1 software. Finally, we study the sensitivity analysis and accordingly present several managerial insights for the benefit of inventory managers. [ABSTRACT FROM AUTHOR]

We first present a notion of a double lacunary sequence on product time scales. Using this notion, we define the notions of the double lacunary statistical convergence and double lacunary strongly p-Cesàro summability of 2-multiple functions on product time scales and we study some fundamental properties of both notions. We also present a theorem that connects the above-mentioned two concepts. Furthermore, we define a refinement of a double lacunary sequence on product time scales and provide some fundamental properties as well as inclusion theorems for a refined and a non-refined double lacunary sequence on product time scales. [ABSTRACT FROM AUTHOR]

In this paper, inspired by the concept of nonlinear elastic matching, generalized metrics, and multiplicative triangle inequality, we propose a bg‐multiplicative metric space in which we propose a generalized notion of a distance function, bg, with degree 2 is a distance of 3 points in generalizing the ordinary distance between 2 points and G‐metric between 3 points. We first discuss bg‐multiplicative metric space mapping and later on the fundamental properties of bg‐multiplicative metric are also discussed. Fundamental properties and several examples for the bg‐multiplicative metric are also given. Moreover, topological properties on the bg‐multiplicative metric space including the convergence of sequences and the continuity of mappings on the bg‐multiplicative metric space are studied. Finally, we generalize some well‐known fixed point theorems including Banach contraction mapping as bg‐multiplicative contraction mapping and proved some fixed point theorems on complete bg‐multiplicative metric spaces. We prove the existence and uniqueness of a solution to a system of bg‐multiplicative integral equations as an application. Our results generalize many pre‐existing results in literature. [ABSTRACT FROM AUTHOR]

This paper studies the state estimation problem for memristor-based stochastic neural networks (MSNNs) with mixed variable delays. A new Lyapunov-Krasovskii functional (LKF) with quadruple integral terms is incorporated. Then, asymptotic stability conditions are estab- lished for the error system using a linear matrix inequality technique. The estimator gain can be obtained by solving the linear matrix inequalities. Numerical simulations are given to demon- strate the effectiveness and superiority of the new scheme. [ABSTRACT FROM AUTHOR]

In this paper, we extend the applications of difference operators and related sequence spaces for the study of the fractional calculus and its dynamics. In this context, some useful results on dynamics of fractional derivatives have been established and demonstrated with the help of existing formulas. Particularly, this study suggests some basic reasons for dynamic behaviors of Riemann‐Liouville fractional derivatives and provides certain idea for neutralizing them. [ABSTRACT FROM AUTHOR]

In this article, we introduce the lacunary difference sequence spaces w0(M, θ, Δnm, p, q), w1(M, θ, Δnm, p, q) and w∞(M, θ, Δnm, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of q-lacunary Δnm-statistical convergent sequences. Further, we study the relationship between q-lacunary n m-statistical convergent sequences and Δnm the spaces w0(M, θ, Δnm, p, q) and w1(M, θ, Δnm, p, q).

This work proposes a modified forward‐backward splitting algorithm combining an inertial technique for solving the monotone variational inclusion problem. The weak convergence theorem is established under some suitable conditions in Hilbert space, and a new step size is presented for our algorithm to speed up the convergence. We give an example and numerical results for supporting our main theorem in infinite dimensional spaces. We also provide an application to predict breast cancer by using our proposed algorithm for updating the optimal weight in machine learning. Moreover, we use the Wisconsin original breast cancer data set as a training set to show efficiency comparing with the other three algorithms in terms of three key parameters, namely, accuracy, recall, and precision. [ABSTRACT FROM AUTHOR]

The Spatio-temporal pattern induced by self-diffusion of a predator-prey model with Boiling type III functional response that incorporates the hunting cooperation between predators has been investigated in this paper. For the local model without structure, the stability of non-negative equilibria with or without collaborative hunting in predators is studied. For the Spatio-temporal model, we analyze the effect of hunting cooperation term on diffusion-driven Turing instability of the homogeneous positive equilibria. To get an idea about patterns formation near the Turing bifurcation, we derive and give a detailed study of the amplitude equation using the multiple-scale analysis. Our result shows that hunting cooperation plays a crucial role in determining the stability and the Turing bifurcation of the model, which is in sharp contrast to the case without cooperation in hunting. Furthermore, some numerical simulations are illustrated to visualize the complex dynamic behavior of the model. [ABSTRACT FROM AUTHOR]

The advantage of various fuzzy normed spaces is to analyse impreciseness and ambiguity that arise in modelling problems. In this paper, various classical stabilities of a new hexic functional equation in different fuzzy spaces like fuzzy Banach space, Felbin's fuzzy Banach space and intuitionistic fuzzy Banach space are presented, concerning the Ulam's theory of stabilities of equations. To validate the stability results, experimental results are presented. Also, a comparative study of the results obtained in this investigation are provided. [ABSTRACT FROM AUTHOR]