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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]

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]

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]