Certain Families Of Integral Operators Research Articles

New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators

In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which appeared recently in the literature on the geometric function theory of complex analysis. We also prove some simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including (for example) a certain μ-convex integral operator and the familiar Bernardi integral operator.

Subordination and superordination preserving properties for families of integral operators for meromorphic functions

In this paper we obtain subordination, superordination, and sandwich-type results related to certain family of integral operators defined on the space of meromorphic functions in the open unit disk. Also, an application of the subordination and superordination theorems to the Gauss hypergeometric function are considered, and the main new results generalize some previously well-known sandwich-type theorems.

A Certain Family of Integral Operators Associated with the Struve Functions

This article presents the study of Struve functions and certain integral operators associated with the Struve functions. It contains the investigation of certain geometric properties like the strong starlikeness and strong convexity of the Struve functions. It also includes the criteria of univalence for a family of certain integral operators associated with the generalized Struve functions. The starlikeness and uniform convexity of the said integral operators are also part of this research.

Inclusion relations for certain families of integral operators associated with conic regions

In this work, we introduce certain subclasses of analytic functions involving the integral operators that generalize the class of uniformly starlike, convex, and close-to-convex functions with respect to symmetric points. We then establish various inclusion relations for these newly defined classes.

An upper bound on the Kolmogorov widths of a certain family of integral operators

We consider the family of integral operators (Kαf)(x) from Lp[0,1] to Lq[0,1] given by (Kαf)(x)=∫01(1−xy)α−1f(y)dy,0<α<1.The main objective is to find upper bounds for the Kolmogorov widths of these operators; these are then used to derive upper bounds for their entropy numbers.We find upper bounds for the nth Kolmogorov widths in question that decrease faster than exp(−κn), and for the nth entropy numbers that decrease faster than exp(−cn3), for some positive constants κ and c.

Certain family of integral operators associated with multivalent functions preserving subordination and superordination

In this paper, we obtain subordination, superordination and sandwich-type results regarding to certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also, an application of the subordination and superordination theorems to the Gauss hypergeometric function are considered. These new results generalize some previously well-known sandwich-type theorems.

Convexity of Integral Operators Involving Dini Functions

In this article, we are mainly interested to find some covexity properties for certain families of integral operators involving Dini functions in the open unit disc. The main tool in the proofs of our results are some functional inequalities of Dini functions. Some particular cases involving Dini functions are also a part of our investigations.

Convergence in variation and a characterization of the absolute continuity

We study approximation results for a family of Mellin integral operators of the form where is a family of kernels, , , and f is a function of bounded variation on . The starting point of this study is motivated by the important applications that approximation properties of certain families of integral operators have in image reconstruction and in other fields. In order to treat such problems, to work in BV -spaces in the multidimensional setting of becomes crucial: for this reason we use a multidimensional concept of variation in the sense of Tonelli, adapted from the classical definition to the present setting of equipped with the Haar measure. Using such definition of variation, we obtain a convergence result proving that , as , whenever f is an absolutely continuous function; moreover we also study the problem of the rate of approximation. In case of regular kernels, we finally prove a characterization of the absolute continuity in terms of the convergence in variation by means of the Mellin-type operators .

Certain family of integral operators preserving subordination and superordination

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.

Convexity of integral operators involving generalized Bessel functions

The main object of this paper is to give sufficient conditions for certain families of integral operators which are defined by means of the normalized form of the generalized Bessel functions to be convex of given order in the open unit disk. In particular cases, we find the corresponding simple conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function.

Some Sufficient Conditions for Univalence of Certain Families of Integral Operators Involving Generalized Bessel Functions

The main object of this paper is to give sufficient conditions for certain families of integral operators, which are defined here by means of the normalized form of the generalized Bessel functions, to be univalent in the open unit disk. In particular cases, we find the corresponding simpler conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function.

Geometric properties of certain non-linear integral operators

In this article, we investigate the mappings of various subclasses of univalent functions by means of certain families of integral operators. Especially, by using the norm estimates of the pre-Schwarzian derivatives, we determine conditions under which these integral operators have geometric meaning associated with the typical subclasses of analytic and univalent functions.

Classes of analytic functions associated with the Choi–Saigo–Srivastava operator

We investigate several properties of the linear Choi–Saigo–Srivastava operator and associated classes of analytic functions which were introduced and studied by J.H. Choi, M. Saigo and H.M. Srivastava [J.H. Choi, M. Saigo, H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276 (2002) 432–445]. Several theorems are an extension of earlier results of the above paper.

Some functional inequalities and inclusion relationships associated with certain families of integral operators

By making use of certain familiar integral operators, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex, and quasi-convex functions. Among other results presented here, the authors establish a number of inclusion relationships associated with some of these integral operators. Some of the results established in this paper would provide extensions of those given in earlier works.

Some inclusion properties of a certain family of integral operators

The authors introduce several new subclasses of analytic functions, which are defined by means of a general integral operator I λ,μ , and investigate various inclusion properties of these subclasses. Many interesting applications involving these and other families of integral operators are also considered.

Certain classes of integral operators associated with the hardy space of analytic functions

This paper is motivated by several recent works studying the mappings of various subclasses of analytic functions by means of certain families of integral operators. The present authors investigate conditions under which some of these integral operators would map starlike and convex functions into the Hardy space H ρ(0 < ρ ≤ ∞) of analytic functions. Some of the main results presented here are also shown to be applicable to certain generalized hypergeometric functions.