Inventory model of deteriorating items for nonlinear holding cost with time dependent demand.

The objective of this model is to investigate the inventory system for perishable items where time proportional deterioration rate is considered. The Economic order quantity is determined for minimizing the average total cost per unit time. Time dependent demand rate is used with finite time horizon. Nonlinear holding cost  with shortage is considered. The result is illustrated with numerical example

LOCAL PROPERTY OF A FACTORED FOURIER SERIES USING ABSOLUTE NORLUND INDEXED-SUMMABILITY

In this paper we have established a theorem on the local property of absolute Norlund indexed-summability of  Factored Fourier series

A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems

Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a Banach space CB(D). Finally, several illustrative examples are presented in light of our definitions and outcomes established in this paper

Model rozmytej ekonomicznej wielkości produkcji funkcji popytu zależną od zmiennej czasu

Background: In this paper, an economic production quantity model is considered under a fuzzy environment. Both the demand cost and holding cost are considered using fuzzy pentagonal numbers. The Signed Distance Method is used to defuzzify the total cost function. Methods: The results obtained by these methods are compared with the help of a numerical example. Sensitivity analysis is also carried out to explore the effect of changes in the values of some of the system parameters. Results and conclusions: The fuzzy EPQ model with time dependent demand rate was presented together with the possible implementation. The behavior of changes in parameters was analyzed. The possible extension of the implementation of this method was presented.Wstęp: W pracy przedstawiono model ekonomicznej wielkości produkcji w rozmytym otoczeniu. Zarówno koszy popytu jak i koszt utrzymania zapasu zostały ujęte, jako rozmyte liczby pentagonalne. Metoda Signed Distance została użyta w celu uszczegółowienia funkcji kosztu całkowitego. Metody: Wyniki otrzymane w obu metodach zostały ze sobą porównane w przykładzie liczbowym. Przeprowadzono analizę wrażliwości w celu określenia wpływu niektórych parametrów na zmiany otrzymywanych wartości. Wyniki i wnioski: Zaprezentowano model ekonomicznej wielkości produkcji funkcji popytu zależnej od zmiennej czasu wraz z możliwym jej zastosowaniem. Przeanalizowano zależności zmian wielkości parametrów. Zaproponowano możliwe rozszerzenie zastosowania tej metody

On Generalized Local Property of ∣A;δ∣k|A;\delta|_{k}-Summability of Factored Fourier Series

The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point and it leads to the local property of Fourier series. In the proposed paper a new result on local property of $|\mathcal{A};\delta|_{k}$-summability of factored Fourier series has been established that generalizes a theorem of Sarig\"{o}l [13] (see [M. A. Sari\"{o}gol, On local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series, \textit{J. Math. Anal. Appl.} 188 (1994), 118-127]) on local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series

On Generalized Local Property of ∣A;δ∣k|A;\delta|_{k}-Summability of Factored Fourier Series

The convergence of Fourier series of a function at a point depends upon the behaviour of the function in the neighborhood of that point and it leads to the local property of Fourier series. In the proposed paper a new result on local property of $|\mathcal{A};\delta|_{k}$-summability of factored Fourier series has been established that generalizes a theorem of Sarig\"{o}l [13] (see [M. A. Sari\"{o}gol, On local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series, \textit{J. Math. Anal. Appl.} 188 (1994), 118-127]) on local property of $|\mathcal{A}|_{k}$-summability of factored Fourier series

An EOQ Model for Items having Fuzzy Amelioration and Deterioration

Due to globalization and modernization, the population of cities is increasing day by day. Also, due to lack of time and work pressure, most of the people living in cities have to depend on different types of food services. To fulfill the requirement of people, the number of hotels, restaurants, and many types of food courts are increasing day by day. All these food-service points mostly depend on chicken, mutton, fish, prawns, and other different types of items that are ameliorating and deteriorating in nature. Keeping this in view, we develop here an inventory model for items that are both ameliorating and deteriorating in a crisp environment. Moreover, the technological development and uncertainty of climate have a great impact on amelioration and deterioration. As such the rate of amelioration and deterioration are of imprecision in nature. Thus, to overcome this situation we also simultaneously discuss a fuzzy model having ameliorating and deteriorating parameters as trapezoidal fuzzy numbers, and the Signed Distance Method is used for defuzzification. Different numerical examples are presented to validate the model. Finally, the sensitivity of important parameters is also studied to draw managerial insight

Statistical deferred weighted B B\mathcal{B}-summability and its applications to associated approximation theorems

Abstract The notion of statistical weighted B $\mathcal{B}$-summability was introduced very recently (Kadak et al. in Appl. Math. Comput. 302:80–96, 2017). In the paper, we study the concept of statistical deferred weighted B $\mathcal{B}$-summability and deferred weighted B $\mathcal{B}$-statistical convergence and then establish an inclusion relation between them. In particular, based on our proposed methods, we establish a new Korovkin-type approximation theorem for the functions of two variables defined on a Banach space CB(D) $C_{B}(\mathcal{D})$ and then present an illustrative example to show that our result is a non-trivial extension of some traditional and statistical versions of Korovkin-type approximation theorems which were demonstrated in the earlier works. Furthermore, we establish another result for the rate of deferred weighted B $\mathcal{B}$-statistical convergence for the same set of functions via modulus of continuity. Finally, we consider a number of interesting special cases and illustrative examples in support of our findings of this paper

The Effectiveness of a Hip Abduction Orthosis for Perthes Disease

Perthes disease is a rare childhood disorder of femoral head affecting 5-10 per 100,000 children. Prognostic factors remain uncertain after age five which requires careful evaluation of subject, planning for treatment always associated with a slow recovery. Orthoses are provided as a conservative treatment to reduce weight bearing stress across hip joint, maintenance of joint congruity, allowing safe and pain free ambulation for school growing children by keeping the limb in abduction and internal rotation. Though there are different number of orthoses used earlier, the present literature does not provide sufficient evidence to support its use in Perthes disease. We report a case of 8 years old active school going subject with Perthes disease of right hip who was fitted with an ambulatory trilateral hip abduction orthosis and assessed by radiographic examination with satisfactory resul