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Co-ordinated convex function of two variables and corresponding inequalities have been studied before by many researchers. This paper deals with Co-ordinated convex function of three variables. In the present paper the idea of co-ordinated convex function of two variables in a rectangle from the plane R² is extended to that of three variables in a rectangle from space R³. Moreover corresponding extended right handed Hermite-Hadamard type inequalities are also incorporated. At the end some applications of resulting inequalities to special means are also given. [ABSTRACT FROM AUTHOR]

In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F,b,ɸ,ρ,θ)- univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F,b,ɸ,ρ,θ)- univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature. [ABSTRACT FROM AUTHOR]

The purposes of this paper are to establish and study the convergence of a new gradient scheme with penalization terms called rapid gradient penalty algorithm (RGPA) for minimizing a convex differentiable function over the set of minimizers of a convex differentiable constrained function. Under the observation of some appropriate choices for the available properties of the considered functions and scalars, we can generate a suitable algorithm that weakly converges to a minimal solution of the considered constraint minimization problem. Further, we also provide a numerical example to compare the rapid gradient penalty algorithm (RGPA) and the algorithm introduced by Peypouquet [20]. [ABSTRACT FROM AUTHOR]

In this paper, we consider the uniqueness problem of admissible functions and non-admissible functions sharing some values in the unit disc. We obtain: If f1 is admissible and f2 is inadmissible satisfying lim r→1- T(r,f2) = ∞, aj(j = 1, 2, ...;q) be q distinct complex numbers. Then (i) f1(z); f2(z) can share at most three values a1, a2, a3 IM; (ii) f1(z); f2(z) can share at most five values aj(j = 1, 2, ...; 5) with reduced weight 1. Our results of this paper are improvement of the uniqueness theorems of meromorphic functions sharing some values on the whole complex plane which given by Yi and Cao. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some argument properties for certain analytic functions in the open unit disk. The main results presented in here generalize some previous those concerning starlike function of reciprocal of order beta and strongly starlike functions. [ABSTRACT FROM AUTHOR]

In this paper we obtain some new inequalities for Heinz operator mean. [ABSTRACT FROM AUTHOR]

In this paper we introduce an argument property which gives an interesting relation between the classes of strongly convex and strongly starlike functions of order α and type β in the open unit disk. Also, the sufficient condition of starlikeness under cer-tain restrictions is obtained. [ABSTRACT FROM AUTHOR]

In this paper the author derives several interesting differential subordination results. These subordinations are established by means of a differential operator obtained using Ruscheweyh derivative Rm f(z) and the multiplier transformations I (m, λ, l) f(z) namely RImα, λ, l the operator given by RImα : An → An, RImα, λ, l f(z) = (1 - α) Rmf(z) + αI (m, λ, l) f(z), for z ∈ U, m ∈ ℝ, λ, l > 0 and An = {f ∈ H(U) : f(z) = z + an+1 + ..., z ∈ 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 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 derive some bounds for the real parts and arguments of the functionals given by ... where Js;b is the widely-investigated Srivastava-Attiya operator defined on the class of normalized analytic functions f in the open unit disk ... with suitable real parameters s and b. These results reduce upon specialization to some well-known inclusion relationships for several classes of functions with given geometric properties. We also make a comparison between one of the results obtained here and an already known result for some specific cases. [ABSTRACT FROM AUTHOR]

In this paper we consider analytic functions in the unit disc D such that |f(p)(z)| is bounded in D. We present several sufficient conditions for function to be p-valent starlike, convex or strongly starlike of a certain order. [ABSTRACT FROM AUTHOR]

In this paper we are interested to give the Hadamard inequality for n-times differentiable convex functions via Caputo fractional derivatives. We also find bounds of a difference of this inequality. [ABSTRACT FROM AUTHOR]

Let A be the class of analytic functions in the open unit disc U with normalization ƒ(0) = ƒ'0 (0) - 1 = 0: The purpose of the present paper is to obtain several sufficient conditions of starlikeness and strongly starlikeness for some subclasses of A with fixed second coefficients that satisfy certain conditions for the quotient of the representations of convexity and starlikeness. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept "strongly extended (s,m)-convex function" and establish some integral inequalities of Simpson's type for strongly extended (s,m)- convex functions. [ABSTRACT FROM AUTHOR]

In this paper we derive the famous Fekete-Szegö inequality for the class of p-valent non-bazilevič function using differential operator. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions as- sociated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

In this paper, we investigate q- analogues of Bieberbach-de Branges theorems and Fekete-Szegö inequalities for certain families of q- convex and q- close-to-convex functions. [ABSTRACT FROM AUTHOR]

In this paper we study certain strong differential superordinations, obtained by using a new integral operator introduced in [13]. [ABSTRACT FROM AUTHOR]

The purpose of the presented paper is to derive several properties and characteristics of analytic functions, by applying the differential subordination techniques. Several consequences of the results stated here are also pointed out. [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, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are (α,m)-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are (α,m)-logarithmically convex functions as special cases. Our results may provide refinements of some results for (α,m)-logarithmically convex functions already exist in the most recent concerned literature of inequalities. [ABSTRACT FROM AUTHOR]

In this paper, operator m-convex and (α,m)-convex function on the co-ordinates are defined, and some new integral inequalities of Hermite-Hadamard type for operator mconvex and (α,m)-convex on the co-ordinates are established. [ABSTRACT FROM AUTHOR]

In this paper, a new general identity for Riemann--Liouville fractional integrals is established. Then by making use of the established identity, we establish some new inequalities of the Simpson and the Hermite--Hadamard type for functions whose absolute values of derivatives are convex. Our results have some relationships with the results, proved in [3, 6, 10], and the analysis used in the proofs is simple. [ABSTRACT FROM AUTHOR]

For functions belonging to the class Sm (δ, α) , δ ∈ [0, 1), α ≥ 0 and m ∈ 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) f(z) namely (These equations cannot be represented into ASCII text), where p, n ∈ ℕ, m ∈ ℕ∪ {0}, λ, l ≥ 0 and f ∈ A(p, n), (These equations cannot be represented into ASCII text). 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]

The purpose of this paper is to establish some new KKM type theorems in G-convex spaces and, as applications, to obtain some new matching theorems, fixed point theorems, section theorems and minimax theorems in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1-6, 16, 20, 23]. [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]

In the paper, the concept of α-logarithmically preinvex function is introduced, and by creating an integral identity involving an n-times differentiable function, some new Hermite-Hadamard type inequalities for α-logarithmically preinvex functions are established. [ABSTRACT FROM AUTHOR]

In this paper, we present the notion of (g, φh,m) -convex and (g, log φ) -convex dominated function and present some properties of them. Besides, we attain some Hermite-Hadamard-type inequalities for (g, φh,m) -convex and (g, log φ) -convex dominated functions. Our results generalize some findings about Hermite-Hadamard-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

In this paper we prove Hermite{Hadamard type inequalities for m-convex and (α,m)-convex functions for fuzzy integrals. Some examples are also given to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper introduces new subclasses of analytic functions and investigate the inclusion properties of these subclasses using the generalized Bessel functions of the first kind. We also derive a variety of special cases and corollaries of the main results. [ABSTRACT FROM AUTHOR]

In this paper, the concept of GA-convex functions on the co-ordinates is introduced. By using a concept of GA-convex functions on the co-ordinates, Hermite-Hadamard type inequalities for this class of functions are settled. [ABSTRACT FROM AUTHOR]

In the paper, by establishing a Riemann-Liouville fractional integral identity involving an n-times differentiable function, the authors present some Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for s-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, authors introduce the concepts of operator m- convex function and operator (α, m)-convex function, and establish some new in- tegral inequalities of Hermite-Hadamard type for operator m-convex and (α, m)- convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate and present several sets of sufficient conditions for Carathéodory functions in the open unit disk U. We then apply the main results proven here in order to derive some conditions for starlike functions in U. Relevant connections with various known results are also considered. [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 distributed algorithm is an important and basic approach, and it is usually used for large scale data processing. This paper aims to error analysis of distributed algorithm for large scale data classification generated from Tikhonov regularization schemes associated with varying Gaussian kernels and convex loss functions. The main goal is to provide fast convergence rates for the excess misclassification error. The number of subsets randomly divided from a large scale datasets is determined to guarantee that the distributed algorithm have lower time complexity and memory complexity. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept geometrically mean convex function on co-ordinates and establish some new integral inequalities of Hermite-Hadamard type for geometrically mean convex functions of two variables on the co-ordinates. [ABSTRACT FROM AUTHOR]

In this paper,we have established some Hermite-Hadamard in-equalities for preinvex functions via fractional integrals and these results have some relationship with the obtained results. Application of the obtained results are given as well. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce a new class of generalized convex functions, called second order (F, α, ρ, d)-V-convex functions and then discuss appropriate duality results for second order Mangasarian type, Mond-Weir type and general Mond- Weir type multiobjective duals. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (h - (α, m))-logarithmically convex functions and establish some new integral inequalities of these classes of functions. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses G(λ, α) and K(λ, α) of analytic functions. [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]

In the present paper, we obtain coefficient inequalities, inclusion relationships involving neighborhoods, subordination results, properties involving modified Hadamard products and also study majorization properties of certain subclasses of multivalent analytic functions, which are defined by means of a certain linear operator. Some useful consequences our main results are mentioned and their relevance with some of the earlier results are also pointed out. [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 the present paper we study the operator using the extended generalized Sălăgean operator and extended Ruscheweyh operator, denote by DRmλ f(z, ς), the Hadamard product of the extended generalized Sălăgean operator Dmλ f(z, ς) and extended Ruscheweyh operator Rmf(z, ς), given by DRmλ f(z, ς):A*ς→A*ς, DRmλ f(z, ς) = Dmλ*Rm f(z, ς) and A*nς={f ∈H(U x ...) : f(z, ς) = z +an-1(ς)zn+1 + ..., z ∈ U, ς ∈ ...}is the class of normalized analytic functions with A*1ς = A*ς. We obtain several strong differential subordinations regarding the operator DRmλ f(z, ς) [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 the paper, the authors introduce a notion "(α, m)-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for (α, m)-GA-convex functions. 2010 Mathematics Subject Classification: Primary 26A51; Secondary 26D15, 26E60, 41A55. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a notion "(α,m)-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for (α,m)-GA-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we define (h -- (α,m))-convex functions that is a new class of convex functions as a generalization of (α, m) --convexity and h --convexity. We also prove some Hadamard's type inequalities. [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]