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In this paper, we study about the q-exponential function which was introduced by Exton. We propose the addition theorem for this q-exponential function and also Continued fraction representation for this q{exponential function is given. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish several new inequalities of the Hermite-Hadamard type for functions whose derivatives are extended s-convex in the absolute value and present some applications to special means of positive real numbers. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRm,nλ,l defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative Rn, given by IRm,n λ,l : A → A, IRm,n λ,l f (z) = (I (m, λ, l) * Rn) 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. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRm,n λ,l and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

In this paper we establish some fuzzy differential subordinations regarding the differential operator RIα m,λ;l : An → An, RIαm,λ,lf(z) = (1 - α)Rmf(z) + αI (m, λ, l) f(z); where Rm is the Ruscheweyh derivative,I (m, λ; l) is the multiplier transformation and An = {f ∊ H(U), f(z) = z +an + 1zn+1 +... , z ∊ U} is the class of normalized analytic functions. We introduce a fuzzy class RIδF (α, m; λ, l) and by using the fuzzy differential subordinations we derive some properties of this class: Also, several fuzzy differential subordinations are established regarding the studied differential operator. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the linear autonomous system of neutral delay diffierential equations with Riemann-Liouville fractional derivative... where Dαx(t) = [Dαx1(t);Dα2x2(t); ...Dαmxm(t)]T is Riemann-Liouville fractional derivative, the coefficients Pj(j =α; 2...l) and Qi(i =α; 2...n) are real m × m matrices and the delays j(j =α; 2 ...l) and #949;i(i α; 2 ...n) are non-negative real numbers. Sufficient conditions for all solutions of the given equation to be oscillatory are obtained by using fractional calculus and Laplace transform. [ABSTRACT FROM AUTHOR]

In this paper, the concept of generalized difference for fuzzy n-cell numbers is presented, and we use the generalized difference to introduce and study the differentiability for fuzzy n-cell mappings. Next, the convexity for fuzzy n-cell mappings is studied, which is based on the concept of the partial ordering of fuzzy n-cell numbers proposed in this study. Finally, using the differentiability and the convexity for fuzzy n-cell mappings, we obtain the KKT optimality conditions for a class of fuzzy constrained minimization problem. [ABSTRACT FROM AUTHOR]

In the present paper we establish several differential superordinations regarding the operator RDλ,αn defined by using Ruscheweyh derivative Rn f (z) andthe generalizedSălăgean operator Dλn f (z), RDλ,αn : A → A, RD RDλ,αn f (z) = (1 - α)Rn f (z) + αDλn f (z),z ∈ - U, where n ∈ ..., λ, α ≥ 0 and f ∈ A, A = {f ∈ H(U) : f (z) = z + ...,z ∈ U}. A number of interesting consequences of some of these superordination 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 this paper, we first prove two Hermite-Hadamard type inequalities for h-preinvex functions via Riemann-Liouville fractional integrals, and then, by introducing an integral identity including the second order derivatives of a given function, we establish some Hermite-Hadamard type inequalities for functions whose second order derivatives are h-preinvex via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the Gronwall-Bellman type inequalities involving the distributional Henstock-Kurzweil integral. Moreover, an linear differential equation with distributional coefficients is considered as an application. [ABSTRACT FROM AUTHOR]

In this paper, we have established the inclusion relations for k-uniformly starlike functions under the (Dqf)(z) operator. We define two new sub-class of k-uniformly starlike functions of order α. Moreover, for functions belonging to these function classes, we investigate necessary and suffcient coeffcient conditions, distortion bounds, extreme points. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of Fibonacci (co-)derivative of real-valued functions. We find general solutions of the equations ▵ (f(x)) = g(x) and (▵ + I)(f(x)) = g(x). [ABSTRACT FROM AUTHOR]

In this paper, we investigate boundedness and compactness of the weighted composition followed and proceeded by differentiation operators from Zygmund spaces to Bers-type spaces and little Bers-type spaces. Some sufficient and necessary conditions for the boundedness and compactness of these operators are obtained. [ABSTRACT FROM AUTHOR]

In this paper we obtain some subordination and superordination results for the operator IRλ.lm,n and we establish di erential sandwich-type theorems. The operator IRλ.lm,n is defined as the Hadamard product of the multiplier transformation I (m, λ l) and Ruscheweyh derivative Rn. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concept of homomorphisms and derivations in intuitionistic fuzzy normed algebras for 2-dimensional functional equations. Furthermore, we investigate the Hyers-Ulam stability bi-homomorphisms and bi-derivations in intuitionistic fuzzy ternary normed algebras concerning a 2-dimensional bi-additive functional equation. [ABSTRACT FROM AUTHOR]

In this paper we obtain some subordination and superordination results for the operator IRm;nλ:l and we establish differential sandwich-type theorems. The operator IRm;nλ:l is defined as the Hadamard product of the multiplier transformation I (m; λ l) and Ruscheweyh derivative Rn. [ABSTRACT FROM AUTHOR]

We study the uniqueness problem of nonlinear differential polynomials of meromorphic functions that share one small function. A uniqueness result which related to multiplicity of meromorphic function is proved in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce general classes of bivariate and Mittag-Leffler functions Eγ1,γ2(α,β,η,ξ,λ) (x, y) and Laguerre polynomials Ln,m(α,β,γ,η,ξ)(x, y). We investigate double fractional integrals and derivative properties of the above mentioned classes. We further obtain linear generating function for Ln,m(α,β,γ,η,ξ)(x, y) in terms of Eγ1,γ2(α,β,η,ξ,λ)(x, y) . Finally, we calculate double Laplace transforms of the above mentioned classes and then we consider a general singular integral equation with Ln,m(α,β,γ,η,ξ)(x, y) in the kernel and obtain the solution in terms of Eγ1,γ2(α,β,η,ξ,λ)(x, y). [ABSTRACT FROM AUTHOR]

In this paper, we introduce twice weakly differentiable and twice H- differentiable interval valued functions. The existence of twice H-differentiable interval-valued function and its relation with twice weakly differentiable func- tions are presented. Interval valued bonvex and generalized bonvex func- tions involving twice H-differentiability are proposed. Under the proposed settings, necessary conditions are elicited naturally in order to achieve LU- efficient solution. Mangasarian type dual is discussed for a nondifferentiable multiobjective programming problem and appropriate duality results are also derived. The theoretical developments are illustrated through non-trivial nu- merical examples. [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRλ,lm,n defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative R¹, given by IRλ,lm,n : A → A, IRλ,lm,n (z) = (I (m, λ, l) * Rn)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. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRλ,lm,n and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass L(d, α, β) of univalent functions defined by the linear operator Lγnf(z) defined by using the Ruscheweyh derivative Rnf(z) and the Sălăgean operator Snf(z), as Lγn : A → A, Lγnf(z) = (1 - γ)Rnf (z)+γSnf(z), z ∈ U, where A„ = {f e H(U) : f(z) = z + an+1zn+1 + ..., z ∈ 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]

A new generalization of the Ostrowski inequality and Ostrowski type inequality for dou-ble integrals on time scales are established in this paper. Several interesting inequalities representing special cases of our general results are supplied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce twice weakly differentiable and twice H-differentiable interval valued functions. The existence of twice H-differentiable interval-valued function and its relation with twice weakly differentiable func-tions are presented. Interval valued bonvex and generalized bonvex func-tions involving twice H-differentiability are proposed. Under the proposed settings, necessary conditions are elicited naturally in order to achieve LU-efficient solution. Mangasarian type dual is discussed for a nondifferentiable multiobjective programming problem and appropriate duality results are also derived. The theoretical developments are illustrated through non-trivial nu-merical examples. [ABSTRACT FROM AUTHOR]

In this paper, due to the theories of normal family and complex differential equation, we consider a uniqueness problem of meromorphic functions share set S = {a, b} with their k-th derivatives. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some identities of Bell polynomials associated with special polynomials which are derived from p-adic integral on Zp. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a viral infection model with humoral immunity. The incidence rate is given by Hill type infection rate. We have derived two threshold parameters, R0 and R1 which completely determined the global properties of the model. By constructing suitable Lyapunov functions and applying LaSalle's invariance principle we have established the global asymptotic stability of all steady states of the model. We have proven that, if R0 ≤ 1, then the infection-free steady state is globally asymptotically stable (GAS), if R1 ≤ 1 < R0, then the chronic-infection steady state without humoral immune response is GAS, and if R1 > 1, then the chronic-infection steady state with humoral immune response is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in [6, 7] and a generalized Mortici's lemma. [ABSTRACT FROM AUTHOR]

In this paper, we consider Choquet integrals and derivatives of non- negative, continuous and decreasing functions on the non-positive real line with respect to fuzzy measures. We prove some properties of derivatives of those functions and some examples. [ABSTRACT FROM AUTHOR]

Several new weighted inequalities connected with Hermite-Hadamard and Fejér type inequalities are established for functions whose derivatives in absolute value are preinvex. The results presented in this paper provide ex- tensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inequalities to derive some inequalities of special means. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the new stability, superstability and hyperstability of the cubic Lie derivations associated with the system of general cubic functional equations: {f(xy) = x³f(y) + f(x)y³, f(x + ky) - kf(x + y)+ kf(x - y) - f(x - ky) = 2k(k² - 1) f(y) in Banach algebras. [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]

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]

Several new weighted inequalities connected with Hermite-Hadamard and Fejér type inequalities are established for functions whose derivatives in absolute value are preinvex. The results presented in this paper provide ex- tensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the new stability, superstability and hyperstability of the cubic Lie derivations associated with the system of general cubic functional equations: ... in Banach algebras. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new inequalities of Simpson type for functions whose third derivatives are extended s-convex functions, and apply these inqualities to derive some inqualitites of special means. [ABSTRACT FROM AUTHOR]

In this paper we introduce new classes containig the linear operator ..., where Rnf(z) is the Ruscheweyh derivative, I (n, λ, l) f(z) the multiplier transformation and ... is the class of normalized analytic functions with A1 = A. Characterization and other properties of these classes are studied. [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 ..., where Rnf(z) is the Ruscheweyh derivative, Snf(z) the Salagean operator and ... 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 .... [ABSTRACT FROM AUTHOR]

In this paper, the following functional equation ... is considered (n ≥ 2), and the Hyers-Ulam stability and superstability of (fr, fs)-double derivations on quasi-Banach algebras associated with the functional equation (0.1) are proved. [ABSTRACT FROM AUTHOR]

Shokri et al. [11] proved the Hyers-Ulam stability of bihomomorphisms and biderivations on normed 3-Lie systems by using the fixed point method. Under the conditions in the main theorems of [11, Section 2], we can show that the related mappings must be zero. In this paper, we correct the statements of the results in [11, Section 2], and prove the corrected theorems. [ABSTRACT FROM AUTHOR]

In this paper, the following functional equation ... is considered (n ≥ 2), and the Hyers-Ulam stability and superstability of (fr, fs)-double derivations on quasi-Banach algebras associated with the functional equation (0.1) are proved. [ABSTRACT FROM AUTHOR]

In this paper, we consider Barnes' multiple Bernoulli and poly-Bernoulli mixedtype polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of three-point boundary value problems of Sequential Derivatives of nonlinear q-difference equations. Our problems contain different numbers of q in derivatives and integrals. By using a variety of fixed point theorems (such as Banach's contraction principle and Krasnoselskii's fixed point theorem, some new existence and uniqueness results are obtained. Illustrative example is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

In this paper, we study some new inequalities of Hermite-Hadamard's type fractional integral inequalities for functions whose absolute values of second derivatives are convex and concave . The obtained results generalize the existing Hermite-Hadamard type integral inequalities and their application in special means and numerical integration. [ABSTRACT FROM AUTHOR]

This paper addresses the approximation by feed-forward neural networks (FNNs) with sigmoidal active functions on the unit sphere. Firstly, some nice properties of typical logistic function are derived, and the function and its derivatives are taken as active functions to construct spherical FNNs approximation operators, where the spherical Cesáro mean is employed as a key link in constructing the operators. Subsequently, by using spherical quadrature formula and Marcinkiewicz-Zygmund type inequality, the error of the operators approximating continuous spherical function is estimated, and a Jackson type theorem is established by means of the best polynomial approximation. [ABSTRACT FROM AUTHOR]

In this paper, we give some interesting and new identities of q-Bernoulli numbers which are derived from convolutions on the ring of p-adic integers. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of ternary Jordan C*-homomorphisms and ternary Jordan C*-derivations associated with the following generalized Cauchy-Jensen functional equation: (*) ... by proving the generalization of Ğavruţa's theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some interesting identities involving r-stirling numbers which are derived from the transfer formula for the associated sequences. [ABSTRACT FROM AUTHOR]