In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...

This paper derives several novel properties of conditional quantiles viewed as nonlinear operators. The results are organized in parallel to the usual expectation operator. We first define a τ-conditional quantile random set, relative any sigma-algebra, set solutions an optimization problem. Then, well-known unconditional quantiles, translation invariance, comonotonicity, and equivariance monot...

In this note, generalized connections σT,f are investigated, where AσT,fB = TAfT − A (B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol T A denotes a reflexive generalized inverse of a positive bounded linear operator TA. The problem of estimating a given generalized connection by other ones is studied. T...

A class of enhancement techniques is proposed for images in arbitrary dimension D. They are free from either space/frequency (scale) or grey references. There are two subclasses. One subclass is the chain: {Negative Laplace operator, Multiplication by Power (γ−1) of modulus-Laplace value, Inverse Negative Laplace operator} together with generalized versions. The generalization of the Negative L...

In this paper, we introduce a linear operator for harmonic multivalent functions by using harmonic convolution operator and generalized Saitoh operator. We investigate some properties of a new subclass of harmonic multivalent functions defined by using this operator.

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...