For μ ≥ 0, we consider a linear operator Lμ : A → A defined by the convolution fμ∗f , where fμ = (1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Let φ∗(A,B) denote the class of normalized functions f which are analytic in the open unit disk and satisfy the condition zf ′/f ≺ (1+Az)/1+Bz, −1 ≤ A < B ≤ 1, and let Rη(β) denote the class of normalized analytic functions f for which there exits a number η∈ (...

Edges represent significant boundary information between objects or classes. Various methods, which are based on differential operation, such as Sobel, Prewitt, Roberts, Canny, and etc. have been proposed and widely used. The methods are based on a linear convolution of mask with pre-assigned coefficients. In this paper, we propose an edge detection method based on Dempster-Shafer's evidence th...

* Correspondence: [email protected] Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan Full list of author information is available at the end of the article Abstract In this investigation, motivated from Breaz study, we introduce a new family of integral operator using famous convolution technique. We also apply this newly defined operator for investigating some inte...

We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that underlies both the theory of Mehler semigroups and operator selfdecomposable measures. We show how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and demonstra...

The problem under consideration relates to a model of a porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency. Then, the associated time-model involves non rational convolution operators, which make the model complex from both analysis and simulation points of view. In this paper, based on the so-called diffu...

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.

In a 1999 paper, Bercovici and Pata showed that a natural bijection between the classically, free and Boolean infinitely divisible measures held at the level of limit theorems of triangular arrays. This result was extended to include monotone convolution by the authors in [AW14]. In recent years, operator-valued versions of free, Boolean and monotone probability have also been developed. Belins...

The pseudodifferential operator (p.d.o.)A(x,D), associated with the Bessel operator d2/dx2 + (1− 4μ2)/4x2, is defined. Symbol class Hm ρ,δ is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian spaceHμ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution Lσ,α-norm continuity of...

Making use of a linear operator, which is defined by the Hadamard product, we introduce and study a subclass Y a,c A,B; p, λ, α of the class A p . In this paper, we obtain the coefficient inequality, distortion theorem, radius of convexity and starlikeness, neighborhood property, modified convolution properties of this class. Furthermore, an application of fractional calculus operator is given....

In the present work, authors introduce a new linear differential operator associated with $ q $-calculus which uses $-derivative operator. For class involving operator, interesting properties like coefficient inequality, growth, distortion, convolution and radii of starlikeness are established. Various connections that earlier works pointed out.