In the present paper, we will study the generalized ( p, q) -type and
generalized lower ( p, q) -type of an entire function in several complex
variables with respect to the proximate order with index pair ( p, q) are
defined and their coefficient characterizations are obtained.

This paper aims at introducing a new generalized differential operator and new subclass of analytic functions to obtain some interesting properties like coefficient estimates and fractional derivatives.

     In the complex field, special functions are closely related to geometric holomorphic functions. Koebe function is a notable contribution to the study of the geometric function theory (GFT), which is a univalent function. This sequel introduces a new class that includes a more general Koebe function which is holomorphic in a complex domain. The purpose of this work is to present a new operator correlated with GFT. A new generalized Koebe operator is proposed in terms of the convolution principle. This Koebe operator refers to the generality of a prominent differential operator, namely the Ruscheweyh operator. Theoretical investigations in this effort lead to a number of implementations in the subordination function theory. The ti

          The present paper studies the generalized Φ-  recurrent of Kenmotsu type manifolds. This is done to determine the components of the covariant derivative of the Riemannian curvature tensor. Moreover, the conditions which make Kenmotsu type manifolds to be locally symmetric or generalized Φ- recurrent have been established. It is also concluded that the locally symmetric of Kenmotsu type manifolds are generalized recurrent under suitable condition and vice versa. Furthermore, the study establishes the relationship between the Einstein manifolds and locally symmetric of Kenmotsu type manifolds.

In this article, a new class  of analytic functions which is defined by terms of a quasi-subordination is introduced. The coefficient estimates, including the classical  inequality of functions belonging to this class, are then derived. Also, several special improving results for the associated classes involving the subordination are presented.

In this paper, we generalize many earlier differential operators which were studied by other researchers using our differential operator. We also obtain a new subclass of starlike functions to utilize some interesting properties.

In this paper, we illustrate how to use the generalized homogeneous -shift operator  in generalizing various well-known q-identities, such as Hiene's transformation, the q-Gauss sum, and Jackson's transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

This article discusses the estimation methods for parameters of a generalized inverted exponential distribution with different estimation methods by using Progressive type-I interval censored data. In addition to conventional maximum likelihood estimation, the mid-point method, probability plot method and method of moments are suggested for parameter estimation. To get maximum likelihood estimates, we utilize the Newton-Raphson, expectation -maximization and stochastic expectation-maximization methods. Furthermore, the approximate confidence intervals for the parameters are obtained via the inverse of the observed information matrix. The Monte Carlo simulations are used to introduce numerical comparisons of the proposed estimators. In ad

      This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.