Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that un...
A unifying
At present, fuzzy modeling has established itself as an effective tool for designing and developing systems for various purposes that are used to solve problems of control, diagnostics, forecasting, and decision making. One of the most important prob...
During the fault period, a phase angle jump may occur at the stator or the point of common coupling, which will deteriorate the low-voltage ride-through (LVRT) characteristics of a doubly fed induction generator (DFIG). The existing LVRT studies focu...
The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–...
The use of physical unclonable functions (PUFs) linked to the manufacturing process of the electronic devices supporting applications that exchange critical data over the Internet has made these elements essential to guarantee the authenticity of sai...
The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the g...
In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-funct...
There are several general concepts that allow obtaining explicit formulas for the coefficients of generating functions in one variable by using their powers. One such concept is the application of compositae of generating functions. In previous studi...
In this paper, we generalize previous results on the generalized stability of the general septic functional equation
Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, cl...
By employing two well-known Euler’s transformations for the hypergeometric function
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to paramet...
In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcenden...
The generalized trigonometric functions called Ateb-functions are considered. On this basis, a generalization of the Fourier transform is constructed and called the Ateb-transform. From the operator theory point of view, the Ateb-transform is conside...
In this article, we introduce the generalized Bessel–Maitland function (EGBMF) using the extended beta function and some important properties obtained. Thus, we first show interesting relationships of this function with Laguerre polynomials and...
Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have...
In this paper, we provide a new bivariate distribution obtained from a Kibble-type bivariate gamma distribution. The stochastic representation was obtained by the sum of a Kibble-type bivariate random vector and a bivariate random vector builded by t...
The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we...
In this paper, we study methods for obtaining explicit formulas for the coefficients of generating functions. To solve this problem, we consider the methods that are based on using the powers of generating functions. We propose to generalize the conc...
Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-gen...
In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized cohere...
Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived usin...
The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of severa...
In this paper, we consider a generalized Mittag-Leffler (ML)-type function and establish several integral formulas involving Jacobi and related transforms. We also establish some of the composition of generalized fractional derivative formulas associ...
One of the main motivations of this paper is to construct generating functions for generalization of the Touchard polynomials (or generalization exponential functions) and certain special numbers. Many novel formulas and relations for these polynomia...
In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measu...
In this paper, we investigate new geometric properties of normalized analytic functions associated with the generalized Marcum Q-function. In particular, we focus on two analytic forms derived from a normalized derivative of a representation involvin...
There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy....
A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality co...
In this paper, we investigate a general multivariable functional equation. We prove, using the fixed-point method, the generalized Hyers–Ulam stability of this equation in Banach spaces. In this way, we obtain sufficient conditions for the stab...
There have been numerous investigations on the hypergeometric series
A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions defined in ∆
We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published pa...
In this paper, we discussed a new subclass
In this paper, we investigate a class of analytic functions associated with the generalized Marcum Q-function and its Alexander transform. We establish sufficient conditions under which these functions exhibit important geometric properties in the op...
The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method. We derive a relation between generat...
Here, we ascertain generalized integral formulas concerning the product of the generalized Mittag-Leffler function. These integral formulas are described in the form of the generalized Lauricella series. Some special cases are also presented in terms...
In this paper, motivated by the modified Tremblay fractional differential operator and the normalized generalized Bessel–Maitland function, we introduce the generalized Bessel–Maitland–Tremblay function via the Hadamard product tran...
Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of general...
In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not...
The paper considers the generalized hypergeometric function
Generalization of the ordinary hyperbolic functions called hyperbolic Ateb-functions is considered. They are the inverse of incomplete Beta-function. These functions are solutions of differential equations, which describe the aperiodic vibration moti...
In a number of problems in applied mathematics, physics (theoretical and mathematical), statistics, and other fields the hypergeometric functions of one and several variables naturally appear. Hypergeometric functions in one and several variables hav...
A pseudorandom sequence is a repeatable sequence with random statistical properties that is widely used in communication encryption, authentication and channel coding. The pseudorandom sequence generator based on the linear feedback shift register ha...
In this paper, we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As an application, new integral representations for the Euler Gamma function are given.
Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas...
In this paper, we study certain geometric properties such as the starlikeness of order
The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generaliz...
We introduce a new methodological approach for the approximation of generalized offset surfaces using smoothing radial basis functions (RBFs). Existing offset surface generation methods often exhibit limitations such as self-intersections and singula...
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