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In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are additionally taken into consideration to show how the findings of this research relate to those of earlier studies. [ABSTRACT FROM AUTHOR]

Owing to the remarkable success of the hypergeometric functions of one variable, the authors present a study of some families of hypergeometric functions of two or more variables. These functions include (for example) the Kampé de Fériet-type hypergeometric functions in two variables and Srivastava’s general hypergeometric function in three variables. The main aim of this paper is to provide several (presumably new) transformation and summation formulas for appropriately specified members of each of these families of hypergeometric functions in two and three variables. The methodology and techniques, which are used in this paper, are based upon the evaluation of some definite integrals involving logarithmic functions in terms of Riemann’s zeta function, Catalan’s constant, polylogarithm functions, and so on. [ABSTRACT FROM AUTHOR]

The objective of this paper is to estimate the sharp bound of the third Hankel determinant for the kth-root transformation to the class of functions whose derivative has a positive real part satisfying the normalized conditions f(0) = 0 and f0(0) = 1 in the open unit disk D:= {z ∊ C: |z| < 1. [ABSTRACT FROM AUTHOR]

This study demonstrates an inventory system with items changing value over time under various realistic environments. It is assumed that the time-varying deterioration rate depending on the maximum lifetime of items and the items exceeding the maximum lifetime are regarded as scarp and no longer serviceable. As a result, the retailer will invest in preservation technology to reduce the reckless deterioration. On the other hand, the retailer receives an upstream advance-cash-credit payment plan from the supplier while offering a downstream cash-credit payment plan to customers to stimulate sales. As above description, we incorporate the relevant phenomena into the proposed inventory model, then the primary objective is to determine the replenishment cycle time and the preservation technology which maximizes the retailer's total profit. Consequently, the contributions of this study have three parts as follows: (1) Addressing the economic (total profit) and technology (preservation technology) impacts simultaneously; (2) The propositions and theorems are derived along with a solution procedure; (3) It is proved that the optimal solution not only exists but also is unique under some conditions. Next, an algorithm is developed which simplifies the search for the sustainable optimal ordering strategies. Numerical examples and a sensitivity analysis are elaborated to validate the mathematical formulation. Findings are summarized and managerial implications are also discussed. [ABSTRACT FROM AUTHOR]

In this study, we propose to introduce and apply an accurate numerical procedure to solve the mathematical model of fractional order, which describes the electrical circuits composed of resistors and inductors (RL) driven by a voltage of the current source. Our research is based on the spectral collocation method, which utilizes the advantageous characteristics of the third‐order Chebyshev polynomials. Some convergence analysis and error theorems are presented. The proposed research concludes by comparing the approximate solutions obtained for the considered model to the exact solution obtained in the classical case. The derived conclusions are further subjected to illustrative graphical and numerical examinations. [ABSTRACT FROM AUTHOR]