Noor Integral Operator Research Articles

FUZZY DIFFERENTIAL SUBORDINATION INVOLVING GENERALIZED NOOR-RUSCHEWEYH OPERATOR

A new operator Lnλ is introduced as a convex combination of Ruscheweyh derivative operator and Noor integral operator on the class A of analytic functions in the open unit disc E. The operator Lnλ is studied using fuzzy set theory and fuzzy differential subordination. All the results proved are sharp. Some interesting special cases are derived as corollaries for particular choices of the functions acting as fuzzy best dominant.

Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator Dτ−λLα,ζm:A→A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator Dτ−λLα,ζm together with a fuzzy set, and we next define a new class of analytic functions denoted by Rϝζ(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, Rϝζ(m,α,δ). The study includes examples that demonstrate the application of the fundamental theorems and corollaries.

Applications of Fuzzy Differential Subordination for a New Subclass of Analytic Functions

This work is concerned with the branch of complex analysis known as geometric function theory, which has been modified for use in the study of fuzzy sets. We develop a novel operator Lα,λm:An→An in the open unit disc Δ using the Noor integral operator and the generalized Sălăgean differential operator. First, we develop fuzzy differential subordination for the operator Lα,λm and then, taking into account this operator, we define a particular fuzzy class of analytic functions in the open unit disc Δ, represented by Rϝλ(m,α,δ). Using the idea of fuzzy differential subordination, several new results are discovered that are relevant to this class. The fundamental theorems and corollaries are presented, and then examples are provided to illustrate their practical use.

A New Subclass of Bi-Univalent Functions Defined by a Certain Integral Operator

We introduce a comprehensive subfamily of analytic and bi-univalent functions in this study using Horadam polynomials and the q-analog of the Noor integral operator. We establish upper bounds for the absolute values of the second and the third coefficients and the Fekete–Szegö functional for the functions belonging to this family. Various observations of the results presented here are also discussed.

A new characterization of (P, Q)-Lucas polynomial coefficients of the bi-univalent function class associated with q-analogue of Noor integral operator

A new characterization of (P, Q)-Lucas polynomial coefficients of the bi-univalent function class associated with q-analogue of Noor integral operator

On geometric properties of certain subclasses of univalent functions defined by Noor integral operator

Abstract In this paper, we investigate subclasses of univalent functions over | z | < 1 \lvert z\rvert<1 , using the characterization of starlikeness and Noor integral operator defined by convolution of analytic functions. We also give coefficient bounds for the class of 𝛼-spiral function of order 𝜌 and 𝑘-uniformly 𝛼-spirallike functions. Moreover, we provide some examples of univalent functions to illustrate our results.

Based on a family of bi-univalent functions introduced through the Faber polynomial expansions and Noor integral operator

<abstract><p>In this study, by using $ q $-analogue of Noor integral operator, we present an analytic and bi-univalent functions family in $ \mathfrak{D} $. We also derive upper coefficient bounds and some important inequalities for the functions in this family by using the Faber polynomial expansions. Furthermore, some relevant corollaries are also presented.</p></abstract>

$ q $-Noor integral operator associated with starlike functions and $ q $-conic domains

<abstract><p>In this paper, we will discuss some generalized classes of analytic functions related with conic domains in the context of $ q $-calculus. In this work, we define and explore Janowski type $ q $-starlike functions in $ q $ -conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness, growth and distortion results for these classes. It is important to mention that our results are generalization of number of existing results.</p></abstract>

On a family of bi-univalent functions related to the Fibonacci numbers

In this study, we construct a new family of holomorphic biunivalent functions in the open unit disc by the help of q-analogue of Noor integral operator, principle of subordination and Fibonacci polynomials. Also we obtain coefficient bounds and Fekete Szegö inequality for functions belonging this family. We have illustrated relevant families and consequences.

A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator

Recently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators and the principle of subordination we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class.

Coefficient inequalities of analytic functions equipped with conic domains involving $q$-analogue of Noor integral operator

The motivation of this paper is to introduce and study a new class of univalent functions equipped with conic type regions. We also investigate a number of useful properties of this class and coefficient estimates for functions. Several consequences of the results are also pointed out.

New subclass of analytic functions defined by $ q $-analogue of $ p $-valent Noor integral operator

<abstract><p>In this paper, we introduce a certain subclass of analytic functions associated with $ q $-analogue of $ p $-valent Noor integral operator in the open unit disc. A variety of useful properties for this subclass are investigated including coefficient estimates and the familiar Fekete-Szeg ö type inequalities. Several known sequences of the main results are also highlighted.</p></abstract>

A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials

A certain subclass of bi-univalent analytic functions introduced by means of the q-analogue of Noor integral operator and Horadam polynomials

Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of the Noor integral operator

In this paper, by using the $(\mathbf{P},\mathbf{Q})$-Lucas polynomials and the $\mathfrak{q}$-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.

On Sandwich Theorem for Certain Subclasses of Symmetric Analytic Functions Associated with Noor Integral Operator

On Sandwich Theorem for Certain Subclasses of Symmetric Analytic Functions Associated with Noor Integral Operator

Differential inequalities imposed by the extended hypergeometric function.

Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit disk, which are acted upon by the generalized Noor integral operator. Some of outcomes improve and generalize previously known outcomes.

On sandwich theorems for higher-order derivatives of multivalent analytic functions associated with the generalized Noor integral operator

In this paper, we obtain some subordination and superordination results for higher-order derivatives of multivalent analytic functions in the open unit disk by generalized Noor integral operator. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

Abstract In this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

Subordination and superordination preserving properties for a family of integral operators involving the Noor integral operator

Abstract In the present paper, we introduce a family of integral operators I p , n , δ λ , μ ( a , b , c ) associate with the Noor integral operator in the open unit disk U = { z ∈ C : | z | 1 } , which is defined by the convolution [ f p , δ μ ( a , b , c ) ( z ) ] ( - 1 ) * f ( z ) , where f p , δ μ ( a , b , c ) ( z ) = ( 1 - μ + δ ) z p 2 F 1 ( a , b ; c ; z ) + ( μ - δ ) z [ z p 2 F 1 ( a , b ; c ; z ) ] ′ + μ δ z 2 [ z p 2 F 1 ( a , b ; c ; z ) ] ″ ( p ∈ N = { 1 , 2 , ⋯ } ; μ , δ ⩾ 0 ; z ∈ U ) . By using the operator I p , n , δ λ , μ ( a , b , c ) , we investigate some subordination and superordination preserving properties for certain classes of analytic and multivalent functions in U . Various sandwich-type results for these multivalent functions are also obtained.

Differential Sandwich Theorems of P-Valent Functions Defined by Noor Integral Operator

In this paper, we obtain sandwich results involving Hadamard product for certain p-valent functions associated with Noor integral operator in the open unit disk.