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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]

Statistical convergence is more extensive than the classical convergence and has recently drawn the recognition of many researchers. The Korovkin-type approximation theorems are usually based on the convergence analysis of sequences of positive linear operators. Gradually, such approximation theorems are extended over more general sequence spaces with several settings via different kinds of statistical summability techniques. In this paper, we introduce presumably a new statistical Riesz-Euler product summability technique to prove a Korovkin-type approximation theorem. Moreover, we demonstrate another result for the rate of statistical convergence under our proposed summability technique. [ABSTRACT FROM AUTHOR]

This paper aims to introduce the notions of deferred Nörlund statistical Riemann integrability and statistical deferred Nörlund Riemann summability for sequence of real-valued functions and to apply them in Korovkin-type new approximations. First, we present an inclusion theorem to understand the connection between these new notions. Then, based on these potential notions we establish new versions of Korovkin-type theorems with three algebraic test functions. Finally, we compute an example, under the consideration of a positive linear operator in association with the Bernstein polynomials to exhibit the effectiveness of our findings. [ABSTRACT FROM AUTHOR]

In this article, we found an undesirable feature in the theory of summability; that is, the Fourier series of 2π$$ 2\pi $$‐periodic functions is uniformly convergent to the functions via the Ceàsro mean. However, it does not preserve the uniform convergence for the arbitrary periodic functions. To overcome this limitation, the objective of the paper is to introduce and study the notion of deferred Ceàsro mean based on the q$$ q $$ integers for the Fourier series of arbitrary periodic functions. We further study the behavior of our proposed method under both ordinary and statistical versions of convergence and accordingly establish two Korovkin‐type approximation theorems for trigonometric test functions. Finally, we also provide some examples with geometrical illustrations in support of the effectiveness of our results established in this work. [ABSTRACT FROM AUTHOR]

In this paper, we investigate and study the notions of statistical product convergence and statistical product summability via deferred Cesàro and deferred Norlund product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two beautiful and definitively useful concepts. Also, based upon our proposed ideas, we demonstrate new thoughtful approximation of Korovkin-type theorems for a martingale sequence over a Banach space. Moreover, we establish that our theorems effectively extend and improve most (if not all) of the previously existing outcomes (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature. [ABSTRACT FROM AUTHOR]

Recently, various deterministic inventory models were developed for deteriorating items with the uniform demand pattern (either increasing or decreasing) throughout the cycle. However, such types of models are not suitable for many real business problems. In particular, the demand patterns of various items are not steady throughout the cycle. In many inventory models, ordinarily, the demand rises first, then it becomes static and finally decreases, and such types of demands can be portrayed by considering trapezoidal functions. Moreover, the costs associated with the inventory become imprecise due to several socio-economical factors. As a result, the optimal solution obtained by the classical inventory model may not fit the actual scenario. Keeping this in view, we develop here an inventory model for deteriorating items having the trapezoidal type of demand function in both crisp and fuzzy environments by considering three possible cases of shortages which are completely backlogged. Furthermore, in view of the comparative study of both scenarios, different data sets of constraints are examined for optimal results. Also, it is observed that the optimal results of the fuzzy model are more appropriate to real-world inventory problems. Finally, in order to strengthen the present investigation, the managerial insight of fluctuation in parameters is presented analytically via sensitivity analysis. [ABSTRACT FROM AUTHOR]