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This research introduced a new method, the Aboodh Tamimi Ansari transform method ( (A T) 2 method), for solving systems of linear and nonlinear fractional partial differential equations. The method combined the Aboodh transform method and the Tamimi Ansari method, allowing for the simultaneous solution of linear and nonlinear terms without restrictions. The Caputo sense was considered for fractional derivatives. The effectiveness of the proposed method was demonstrated through numerical solutions, graphical representations, and tabular data, showing strong agreement with exact solutions. The approach was deemed precise, easy to apply, and could be extended to address further challenges in fractional-order problems. Computational tasks were carried out using Mathematica 13. [ABSTRACT FROM AUTHOR]

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how glucose excess, estrogen excess, and anxiety work together to affect the speed at which breast cancer cells multiply and the immune system's response model is necessary to conceive of ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological panic, glucose excess, and estrogen excess on the interaction of cancer and immunity. The proposed model is precisely described. The focus of the model's dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish four equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The transcritical bifurcation occurs when the glucose excess is taken as a bifurcation point. Numerical simulations are employed to validate the theoretical study, which shows that psychological panic, glucose excess, and estrogen excess could be significant contributors to the spread of tumors and weakness of immune function. [ABSTRACT FROM AUTHOR]

In this paper, the research discussed involves fractional calculus applied to a q -operator. Fractional integrals applied to the q -analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research. In this paper, the research discussed involves fractional calculus applied to a -operator. Fractional integrals applied to the -analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research. [ABSTRACT FROM AUTHOR]

In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the q -analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc U which is defined and investigated here by using this q -operator. [ABSTRACT FROM AUTHOR]

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided. [ABSTRACT FROM AUTHOR]

The development of certain aspects of geometric function theory after incorporating fractional calculus and q-calculus aspects is obvious and indisputable. The study presented in this paper follows this line of research. New results are obtained by applying means of differential subordination and superordination theories involving an operator previously defined as the Riemann- Liouville fractional integral of the q-hypergeometric function. Numerous theorems are stated and proved involving the fractional q-operator and differential subordinations for which the best dominants are found. Associated corollaries are given as applications of those results using particular functions as best dominants. Dual results regarding the fractional q-operator and differential superordinations are also considered and theorems are proved where the best subordinants are given. Using certain functions known for their remarkable geometric properties applied in the results as best subordinant, interesting corollaries emerge. As a conclusion of the investigations done by applying the means of the two dual theories considering the fractional q-operator, several sandwich-type theorems combine the subordination and superordiantion established results. [ABSTRACT FROM AUTHOR]

In this paper we have discussed differential subordination properties associated with the fractional integral by using Dziok-Srivastava operator. [ABSTRACT FROM AUTHOR]

In the present paper we establish several fuzzy differential subordinations regardind the operator I (m, λ l), given by I (m, λ l) : A → A, I (m, λ l) f (z) = z + Wε1;∞ j=ε (1+λ(j-1)+l /l+1)m ajzj and A = {f ε H(U), f(z) = z + a2z2 +…z … U} is the class of normalized analytic functions. A certain fuzzy class, denoted by SIδF (m, λ l), of analytic functions in the open unit disc is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class SIδF (m, λ l) : Also, several fuzzy differential subordinations are established regarding the operator I (m; λ l). [ABSTRACT FROM AUTHOR]

this paper we have introduced and studied the subclass L(d, α, β) of univalent functions defined by the linear operator Lnʏ f(z) defined by using the Ruscheweyh derivative Rnf(z) and the Să lăgean operator Snf(z), as Lnʏ : A → A, Lnʏ f(z) = (1- ʏ)Rnf(z)+ʏSnf(z), z ϵ U, where An = {f ϵ H(U) : f(z) = z+an+1zn+1 + . . . , z ϵ U} is the class of normalized analytic functions with A1 = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class L(d, α, β). [ABSTRACT FROM AUTHOR]

The main object of this paper is to study some properties of certain subclass of analytic functions in the open unit disc which is defined by the linear operator Lαn : A → A, Lαnf(z) = (1 - α)Rnf(z) + αSnf(z), z ∈ U, where Rnf(z) is the Ruscheweyh derivative, Snf(z) the Sălăgean operator and An = {f ∈ H(U) : f(z) = z + an+1zn+1 + ..., z ∈ U} is the class of normalized analytic functions with A1 = A. These properties include a coefficient inequality, distorsion theorem and extreme points of differential operator. We also discuss the boundedness properties associated with partial sums of functions in the class TSαn (β, γ) . [ABSTRACT FROM AUTHOR]

In this paper we introduce new classes containig the linear operator RIn, λ, lα : A → A, RIn, λ, lα f(z) = (1 - α)Rnf(z) + αI (n, λ, l) f(z), ∈ U, where Rnf(z) is the Ruscheweyh derivative, I (n, λ, l) f(z) the multiplier transformation and An = {f ∈ H(U) : f(z) = z + an+1zn+1 + ..., z ∈ U} is the class of normalized analytic functions with A1 = A. Characterization and other properties of these classes are studied. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass RJ(d, α, β) of univalent functions defined by the linear operator RIγn,λ,lf(z) defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n,λ,l) f(z), as RIγn,λ,l : A → A, RIγn,λ,lf(z) = (1-γ)Rnf(z) + γI (n,λ,l) f(z), zϵ U, where An = {fϵH(U) : f(z) = z+an+1zn+1+ . . . , z ϵ U} is the class of normalized analytic functions with A1 = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class RJ(d, α, β). [ABSTRACT FROM AUTHOR]

The main object of this paper is to study some properties of certain subclass of analytic functions in the open unit disc which is defined by the linear operator RDλ, αn : A → A, RDλ, αn (z) = (1 - α)Rn f(z) + αDλn f(z), z ∈ U, where Rn f(z) is the Ruscheweyh derivative, Dλn f(z) the generalized Sălăgean operator and An = {f ∈ H(U) : f(z) = z + an+1zn+1 ..., z ∈ U} is the class of normalized analytic functions with A1 = A. These properties include a coefficient inequality, distorsion theorem and extreme points of differential operator. We also discuss the boundedness properties associated with partial sums of functions in the class TSλ, αn (β, γ) . [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass RD(d, α, ß) of univalent functions defined by the linear operator RDnλδ f(z) defined by using the Ruscheweyh derivative Rnf(z) and the generalized Salagean operator Dn955f(z), as RDnλ,α : A → A, RDnλδf (z) = (1-y) Rn f(z) + yDnλf(z), z ∈ U, where An = {f ∈ H(U) : f (z) = z + an+1zn+1 + . . . , z ∈ U} is the class of normalized analytic functions with AI = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class RD(d, α, β). [ABSTRACT FROM AUTHOR]

In the present paper we define a new operator using the generalized Sălăgean and Ruscheweyh operators. Denote by DRmλ the Hadamard product of the generalized Sălăgean operator Dmλ and the Ruscheweyh operator Rm, given by DRmλ : An ℯ An, DRmλ f(z) = (Dmλ * Rm) f(z) and An = {f ∈ H(U); f(z) = z + an + 1zn+1 + ..., z ∈ U} is the class of normalized analytic functions. We study some differential superordinations regarding the operator DRmλ. [ABSTRACT FROM AUTHOR]

Let A(p, n) denote the class of normalized analytic functions f(z) in the open unit disc f(z) = zp + ... ak zk, p, n ∈ ℕ := {1, 2, 3,...}. We consider in this paper the operator RIpγ (m, λ, l) f(z) := (1 - γ) Dm f(z) + γIp (m, λ, l) f(z) where Ip (m, λ, l) f(z) = zp + ∑k = p + n∞ [p + λ(k - p) + l/p + l]m ak zk and (m + 1) Dm + 1 f(z) = z(Dm f (z))' + m Dm f(z), m ∈ ℕ0, ℕ0 = ℕ ∪ {0}, λ ∈ ℝ, λ ≥ 0, l ≥ 0 is the Ruscheweyh operator. By making use of the above mentioned differential operator, a new subclass of p--valent functions in the open unit disc is introduced. The new subclass is denoted by ALpγ (m, n, µ, α, λ l). Parallel results, for some related classes including the class of starlike and convex functions respectively, are also obtained. [ABSTRACT FROM AUTHOR]

In this paper we obtain sufficient conditions for univalence of analytic functions defined by the linear operator RI αn, λ, l: A → A, RI αn, λ, lf(z) = (1 - α)Rnf(z), z ∈ U, where Rnf(z) is the Ruscheweyh derivative, I (n, λ, l) the multiplier transformation and An = {f ∈ H (U) : f(z) = z + an+1zn+1 + …, z ∈ U} is the class of normalized analytic functions with A1 = A. [ABSTRACT FROM AUTHOR]

In this paper we establish several fuzzy differential subordinations regarding the operator defined as Hadamard product of Salagean operator Sm and Ruscheweyh derivative Rm. denoted SRm. given by SRm : A → A, SRm f (z) = (Sm " Rm) f (z) and An = (f ∈ H(U), f(z) = z + an+1zn+1 + ..., z ∈ U) is the class of normalized analytic functions with A1 = A. A certain fuzzy class, denoted by SRFm (δ), of analytic functions in the open unit disc is introduced by means of this operator. By making use of the concept, of fuzzy differential subordination we will derive various properties and characteristics of the class SRFm (δ). Also, several fuzzy differential subordinations are established regarding the operator SRm. [ABSTRACT FROM AUTHOR]

In the present paper we establish several fuzzy differential subordinations regardind the operator RDmλ,α. given by RDmλ,α : An -→ An, RDmλ,α = (l-α)Rmf(z)+αDmλf(z)-. where Rmf(z) denote the Ruscheweyh derivative, RDmλ f(z) is the generalized Sǎlǎgean operator and An = {f ∈013; H(U), f(z) = z+an+1zn+1+..., z ∈ U} is the class of normalized analytic functions with A1 = A, A certain fuzzy class, denoted by RDFm (δ, λ, α). of analytic functions in the open unit disc is introduced by means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class RDFm (δ, λ, α). Also, several fuzzy differential subordinations are established regarding the operator RDmλ,α. [ABSTRACT FROM AUTHOR]

The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions to belong to this class are determined and the class is investigated considering aspects regarding coefficient bounds as well as partial sums of these functions. Distortion properties of the functions belonging to the class are proved and radii estimates are established for starlikeness and convexity properties of the class. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential superordinations regardind the new operator DRλm defined by convolution product of the extended Sălăgean operator and Ruscheweyh derivative, DRλm : A*nζ → A*nζ, DRλm f (z, ζ) = (DRλm Rm) f (z, ζ) , z ∈ U, ζ ∈ U, where Rmf(z, ζ) denote the extended Ruscheweyh derivative, Dm λ f(z, ζ) is the extended generalized Sălăgean operator and A nζ = {f ζ H(U × Ū), f(z, ζ) = z + an+1 (ζ) zn+1 + … , z ζ U, ζ ∈ U} is the class of normalized analytic functions. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential subordinations regarding the operator I(m, λ, l), given by I(m, λ, l):Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed, where m ∈ ℕ∪ {0}, λ, l ≥ 0 and A*nζ = {f ∈ H(U x U̅), f(z, ζ) = z + an+1 (ζ) zn+1 +…, z ∈ U, ζ ∈ U̅} is the class of normalized analytic functions. [ABSTRACT FROM AUTHOR]

In the present, paper we establish several strong differential subordinations regardind the new operator Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed, given by Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.: denote the Ruscheweyh derivative, Sn f(z, ζ) is the Sălăgean operator and 휜*nζ = {f ∈ 휢(U x U̅), f(z, ζ) = z + αn+1 (ζ) zn+1 +…, z ∈ U, ζ ∈ U̅} is the class of normalized analytic functions with 휜*1ζ = 휜*ζ. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential superordinations regardind the new operator DR Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. defined by convolution product of the extended generalized Sălăagean operator and Ruscheweyh derivative, DR Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. : 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. → 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. DR Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. (z, ζ ) = (D Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.* Rm f (z; ζ) ; where Rm f(z, ζ) denote the extended Ruscheweyh derivative, D Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. f(z, ζ) is the extended generalized Sălăgean operator and 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.ζ = {f ∈ 횮(U x Ū), f(z, ζ) = z + an+1 (ζ) z n+1 +…, z ∈ U, ζ, ∈ Ū}, with 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.ζ = 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., is the class of normalized analytic functions. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential superordinations regardind the new operator SRm defined by convolution product of the extended Sălăgean operator and Ruscheweyh derivative, SRm : 효Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.ζ → 효 Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. ζ, SRmf (z, ζ) = Sm * Rm) f (z, ζ), z ∈ U, ζ ∈ Ū, where Rm f(z, ζ) denote the extended Ruscheweyh derivative, Sm f(z; ζ) is the extended Sălăagean operator and 효Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.ζ = {f ∈ 횮(U x Ū); f(z,ζ) = z + an+1 (ζ) z n+1 +…, z ∈ U, ζ ∈ Ū is the class of normalized analytic functions. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential subordinations regarding the new operator RIαm,λt, given by RIαm,λt, : A*nζ → A*nζ, RIαm,λtf(z, ζf) = (1 - α)Rmf(z, ζ), where Rmf(z, ζ) denote the Ruscheweyh derivative, I (m, λ, l) is the multiplier transformation and A*nζ = {f ∈ H(U x U̅), f(z, ζ) = z + an+1 (ζ) zn+1 + …, z ∈ U, ζ ∈ U̅} is the class normalized analytic functions. A certain subclass, denoted by RIm (δ, λ, l, α, ζ), of analytic functions is introduced by means of the new operator. [ABSTRACT FROM AUTHOR]

In the present paper we establish several strong differential subordinations regarding the new operator RDnλα, given by RD RDnλα : A*ς → A*ς, RDnλα f (z, ς) = (1 - α) Rn f(z, ς) + α Dn&lambda f(z, ς), where Rn f(z, ς) denote the Ruscheweyh derivative, Dnλ f(z, ς) is the generalized Sălăgean operator and A*nς = {f ∈ H(U x U̅), f(z, ς) = z + an+1 (ς) zn+1 + …, z ∈ U, ς U̅} is the class of normalized analytic functions with A*1ς = A*ς. A certain subclass, denoted by RDn (δ, λ, α), of analytic functions is introduced by means of the new operator. [ABSTRACT FROM AUTHOR]

In the present paper we define a new operator using the multiplier transformation and Ruscheweyh derivative. Denote by RIn,λ,lα the operator given by RIn,λ,lα A → A, RIn,λ,lα f (z) = (1-α)Rn f(z)+αI(n, λ, l) f (z); for z ∈ U; where Rn f (z) denote the Ruscheweyh derivative, I (n, λ, l) f (z) is the multiplier transformation and An = {f ∈ H(U) : f (z) = z + an+1zn+1 + …, z ∈ U} is the class of normalized analytic functions with A1 = A. A certain subclass, denoted by RJn (δ, λ, l, α), of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class RJn (δ, λ l, α). Also, several differential subordinations are established regardind the operator RIn,λ,lα. [ABSTRACT FROM AUTHOR]

In the present paper we define a new operator, by means of convolution product between Ruscheweyh operator and the multiplier transformation I (m, λ, l). For functions f belonging to the class An we define the differential operator IRmλ,l : An → An, IRmλ,lf (z) := (I (m, λ, l) * Rm) f (z) , where An = {f ϵ H(U) : f(z) = z+an+1zn+1+…, z ϵ U} is the class of normalized analytic functions. We study some differential superordinations regarding the operator IRm λ,l. [ABSTRACT FROM AUTHOR]

For functions belonging to the class Sm (δ, α), δ ϵ [0, 1), α ≥ 0 and in ϵ N, of normalized analytic functions in the open unit disc U, which are investigated in this paper, the author derives several interesting differential subordination results. These subordinations are established by means of a special case of the multiplier transformations Ip (m, λ, l) ƒ(z) namely >>>>>Ip (m, λ, l) ƒ(z) ≔ zp + Σj=p+n∞ (p + λ(j - 1) + l/p + 1)m ajzj, where p, n ϵ N, m ϵ NU {0}, λ, l ≥ 0 and ƒ ϵ A(p,n), A (p,n) = {ƒ ϵ H(U) : ƒ(z) = zp + Σj=p+n∞ ajzj, z ϵ U). A number of interesting consequences of some of these subordination results are discussed. Relevant connections of some of the new results obtained in this paper with those in earlier works are also provided. [ABSTRACT FROM AUTHOR]

In the present paper we define a new operator, by means of convolution product between Ruscheweyh operator and the multiplier transformation I (m, λ, l). For functions ƒ belonging to the class A we define the differential operator IRλ,tm : A → A, IRλ,tmƒ (z) := (I (m, λ, l) * Rm) ƒ(z) where An = {ƒ ∈ H(U) ƒ(z) = z + αn+1zn+1 + ߪ, z ࢠ U} is the class of normalized analytic functions with A1 = A. We study certain differential subordinations regarding the operator IRλ,tm. [ABSTRACT FROM AUTHOR]

We propose, in the present paper, to derive some differential subordination results. The work is developed in the case of analytic functions defined on the open unit disc. The results will be formulated by making use of an Atangana–Baleanu fractional integral operator and Bessel functions. For the newly obtained theorems, certain interesting consequences are also considered. Univalent function selections with specific symmetry properties were involved. [ABSTRACT FROM AUTHOR]

We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator Γ π , ρ , β , μ f z . Relevant connections between the new results presented here and those considered in previous works are addressed. The properties and results concerning the differential subordination theory are symmetric to the properties obtained using the differential superordination theory, and by combining them, sandwich-type theorems are obtained. [ABSTRACT FROM AUTHOR]

In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f (z) = z + ∑ n = 2 ∞ a n z n ,   (z ∈ U) . Some new results on differential subordination with some corollaries are obtained. These properties and results are symmetry to the properties of the differential superordination to form the sandwich theorems. [ABSTRACT FROM AUTHOR]

The operator defined as the fractional integral of confluent hypergeometric function was introduced and studied in previously written papers in view of the classical theory of differential subordination. In this paper, the same operator is studied using concepts from the theory of fuzzy differential subordination and superordination. The original theorems contain fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. Interesting corollaries are obtained for particular choices of the functions acting as fuzzy best dominant and fuzzy best subordinant. A nice sandwich-type theorem is stated combining the results given in two theorems proven in this paper using the two dual theories of fuzzy differential subordination and fuzzy differential superordination. [ABSTRACT FROM AUTHOR]

In this paper, two new integral operators are defined using the operator D R λ m , n , introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator D R λ m , n are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new subclasses R Σ , b , c μ , α λ , δ , τ , Φ and K Σ , b , c μ , α λ , δ , η , Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a 2 and a 3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses R Σ , b , c μ , α λ , δ , τ , Φ and K Σ , b , c μ , α λ , δ , η , Φ , as there is a symmetry for the estimations of the coefficients a 2 and a 3 for all the subclasses defind in our this paper. [ABSTRACT FROM AUTHOR]

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator L α m , given by L α m : A n → A n , L α m f (z) = (1 − α) R m f (z) + α S m f (z) , where A n = { f ∈ H (U) , f (z) = z + a n + 1 z n + 1 + ... , z ∈ U } is the subclass of normalized holomorphic functions and the operators R m f (z) and S m f (z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator L α m , a certain fuzzy class of analytic functions denoted by S L F m δ , α is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries. [ABSTRACT FROM AUTHOR]

Here, we study strong differential subordinations for the extended new operator I R λ , l m defined by the Hadamard product of the extended multiplier transformation I m , λ , l and the extended Ruscheweyh derivative R m , on the class of normalized analytic functions A n ζ ∗ = { f ∈ H (U × U ¯) , f (z , ζ) = z + a n + 1 ζ z n + 1 + ⋯ , z ∈ U , ζ ∈ U ¯ } , by I R λ , l m : A n ζ ∗ → A n ζ ∗ , I R λ , l m f z , ζ = I m , λ , l ∗ R m f z , ζ. [ABSTRACT FROM AUTHOR]

An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results. [ABSTRACT FROM AUTHOR]

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. [ABSTRACT FROM AUTHOR]

In [1] and [6] Marx and Strohhäcker have proved that if f ∊ A is a convex function, then it has the property of starlikeness of order 1/2 . In [5, Theorem 9.5.6], P. T. Mocanu extended this result to the class A2 for a convex function of order - 1/2 . In this paper we extend the results proven by Marx and Strohhäcker and by P. T. Mocanu and we'll prove that, if the function f ∊ An, n ≥ 3, is a close-to-convex function, then it is starlike of order 1/2 . [ABSTRACT FROM AUTHOR]