Search

In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 2018, Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find coefficient estimates for the class of functions ℳ N (γ , ϑ , λ) consisting of analytic functions f normalized by f(0) = f′(0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a2, a3, and the Fekete-Szegő functional upper bound for f ∈ ℳ N (γ , ϑ , λ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the singular k-Hessian equations S k ⁢ (λ ⁢ (D 2 ⁢ u)) = h ⁢ (x) ⁢ f ⁢ (- u) + g ⁢ (| D ⁢ u |) in ⁢ Ω and S k ⁢ (λ ⁢ (D 2 ⁢ u)) = h ⁢ (x) ⁢ f ⁢ (- u) ⁢ (1 + g ⁢ (| D ⁢ u |) ) in ⁢ Ω with the Dirichlet boundary condition u = 0 on ∂ ⁡ Ω , where Ω ⊂ ℝ N ( N ≥ 2 ) is a strictly convex, bounded smooth domain. Using the method of upper and lower solutions and the Karamata regular variation theory, we get new criteria of the existence and asymptotic behavior of strictly convex solutions under different conditions imposed on h, f and g. This problem is more difficult to solve than the k-Hessian problem without gradient terms, and requires additional new conditions in the proof process. [ABSTRACT FROM AUTHOR]

In this paper, we first define ray increasing and decreasing monotonicity of maps. If 푇 is an optimal transport map for the Monge problem with cost function ∥ y - x ∥ sc in R n or 푇 is an optimal transport map for the Monge problem with cost function d ⁢ (x , y) , the geodesic distance, in more general, non-branching geodesic spaces 푋, we show respectively equivalence of some previously introduced monotonicity properties and the property of ray increasing as well as ray decreasing monotonicity which we define in this paper. Then, by solving secondary variational problems associated with strictly convex and concave functions respectively, we show that there exist ray increasing and decreasing optimal transport maps for the Monge problem with cost function ∥ y - x ∥ sc . Finally, we give the classification of optimal transport maps for the Monge problem such that the cost function ∥ y - x ∥ sc further satisfies the uniform smoothness and convexity estimates. That is, all of the optimal transport maps for such Monge problem can be divided into three different classes: the ray increasing map, the ray decreasing map and others. [ABSTRACT FROM AUTHOR]

In this paper, we study the higher-order Schwarzian derivative Sn(f) proposed by H. Tamanoi [Higher Schwarzian operators and combinatorics of the Schwarzian derivative, Math. Ann. 305 (1996), 127–151]. For the strongly starlike functions of order α and strongly convex functions of order α, the sharp bound of |S3(f)(0)| is obtained. When n ∈ [2, 7], we prove that the higher Bers maps induced by Sn(f) on Weil-Petersson Teichmüller space and BMO-Teichmüller space are holomorphic. [ABSTRACT FROM AUTHOR]

In this paper, an equality is proved for twice differentiable convex functions involving Riemann–Liouville fractional integral. With the help of this equality, there are established several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann–Liouville fractional integral. [ABSTRACT FROM AUTHOR]

Content industries have several profit sources that positively interact with one another, and piracy affects them not only negatively but also positively. For copyright holders, choosing to allow piracy depends upon its total external effects. This paper proves that in such case the profit function is convex with respect to the level of enforcement. This paper shows a convex profit function with respect to the level of enforcement. The convexity leads to a corner solution of optimal enforcement for copyright holders. Which corner solution is selected depends on the relative size of the sub-market, and no enforcement is profitable if the submarket size is relatively large. This result compensates for a shortcoming of discussions that assume only two options regarding the level of enforcement, zero or perfect enforcement. [ABSTRACT FROM AUTHOR]

In [Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions, J. Funct. Spaces 2021 (2021), Art. ID 6690027], Alimohammadi et al. presented a few conjectures for the logarithmic coefficients γn of the functions f belonging to some well-known classes like C (1 + α z) for α ∈ (0, 1], and C V h p l (1 / 2). For example, it is conjectured that if the function f ∈ C (1 + α z) , then the logarithmic coefficients of f satisfy the inequalities | γ n | ≤ α 2 n (n + 1) , n ∈ N. Equality is attained for the function Lα, n, that is, log L α , n (z) z = 2 ∑ n = 1 ∞ γ n (L α , n) z n = α n (n + 1) z n + ... , z ∈ U. The aim of this paper is to confirm that these conjectures hold for the coefficient γn0−1 whenever the function f has the form f (z) = z + ∑ k = n 0 ∞ a k z k , z ∈ U for some n 0 ∈ N , n0⩾2. [ABSTRACT FROM AUTHOR]

In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with Hankel determinants for starlike and convex functions related to modified sigmoid functions. Sharp bounds are given for second and third Hankel determinants. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some norm inequalities involving convex and concave functions, which are the generalizations of the classical Clarkson inequalities. Let A1, . . . , An be bounded linear operators on a complex separable Hilbert space H and let α1, . . ., αn be positive real numbers such that ∑j=1nαj = 1. We show that for every unitarily invariant norm, If ƒ is a non-negative function on [0, ∞) such that ƒ(0) = 0 and g(t) = ƒ(t) is convex, then |||∑j=1nαjƒ(|Aj|)||| ≥ |||∑j,k∈Sℓ (ƒ(√αjαk /4αℓ(1−αℓ)| Aj + Ak − 2 ∑j=1nαjAj|) + ƒ(√αjαk(2αℓ−1)/4αℓ(1−αℓ)| Aj − Ak|)) + ƒ(|∑j=1nαjAj|)||| for ℓ = 1, . . . , n. If ƒ is a non-negative function on [0, ∞) such that g(t) = ƒ(√t) is concave, then the inverse inequality holds. Here, the symbol Sℓ = {1, . . . , n} ∖ {ℓ} for ℓ ∈ {1, . . . , n}. In addition, we provide some applications of the above inequalities. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre–Pólya class plays a significant role in this paper. Moreover, the interlacing properties of the zeros of the k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler–Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H2,2 or H3,1 over different subclasses of 𝒮. Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 of typically real functions. The second object of our interest is 𝒦ℝ(i), the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the following subclass ... of analytic functions, ┅ is an analytic function with positive real part in the unit disk D, satisfying ┅(0) = 1, ┅(0) > 0, and ┅(D) is symmetric with respect to the real axis. We obtain the upper bound of the second Hankel determinant a2a4-a2/3 -- for functions belonging to the this class is studied using Toeplitz determinants. The results, which are presented in this paper, would generalize those in related works of several earlier authors. [ABSTRACT FROM AUTHOR]

In this paper we introduce some new subclasses of the p-valent analytic functions with higher-order derivatives that generalize some related subclasses of starlike and convex functions of a positive order. We found the order of (p,q)-valent starlikeness and convexity for the products of functions that belong to these classes. The order of (p,q)-valent starlikeness and convexity of certain integral operators for the product of functions of these classes were also obtained. [ABSTRACT FROM AUTHOR]

This paper studies analytic functions f defined on the open unit disk of the complex plane for which f/g and (1 + z)g/z are both functions with positive real part for some analytic function g. We determine radius constants of these functions to belong to classes of strong starlike functions, starlike functions of order α, parabolic starlike functions, as well as to the classes of starlike functions associated with lemniscate of Bernoulli, cardioid, lune, reverse lemniscate, sine function, exponential function and a particular rational function. The results obtained are sharp. [ABSTRACT FROM AUTHOR]

In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingredients in the arguments. Furthermore, the asymptotic behavior of nontrivial radial convex solutions for Monge-Ampère systems is also considered. Finally, as an application, we obtain sufficient conditions for the existence of nontrivial radial convex solutions of the power-type system of Monge-Ampère equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize several differential subordination results, involving arithmetic, geometric and harmonic means of the expressions p(z) and p (z) + z p ′ (z) p (z). $\begin{array}{} p(z)+\frac{zp'(z)}{p(z)}. \end{array} $ Are also given certain applications of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the fractional Hermite-Hadamard inequality on , where is a set of positive real numbers such that for . Using this inequality, we present a new characterization of convexity of a function defined on . [ABSTRACT FROM AUTHOR]

We consider the long-time behavior of a nonlinear PDE with a memory term which can be recast in the abstract form d/dt ρ(ut) + Autt + γAɵut + Au - t ∫ 0 g(s)Au(t - s) = 0, where A is a self-adjoint, positive definite operator acting on a Hilbert space H, ρ(s) is a continuous, monotone increasing function and the relaxation kernel g(s) is a continuous, decreasing function in L1(R+) with g(0) > 0. Of particular interest is the case when A = -▵ with appropriate boundary conditions and ρ(s) = ∣s∣ρs. This model arises in the context of solid mechanics accounting for variable density of the material. While finite energy solutions of the underlying PDE solutions exhibit exponential decay rates when strong damping is active (γ > 0, θ = 1), this uniform decay is no longer valid (by spectral analysis arguments) for dynamics subjected to frictional damping only, say, θ = 0 and g = 0. In the absence of mechanical damping (γ = 0), the linearized version of the model reduces to a Volterra equation generated by bounded generators and, hence, it is exponentially stable for exponentially decaying kernels. The aim of the paper is to study intrinsic decays for the energy of the nonlinear model accounting for large classes of relaxation kernels described by the inequality g' + H(g) ≤ 0 with H convex and subject to the assumptions specified in (1.13) (a general framework introduced first in [1] in the context of linear second-order evolution equations with memory). In the context of frictional damping, such a framework was introduced earlier in [15], where it was shown that the decay rates of second-order evolution equations with frictional damping can be described by solutions of an ODE driven by a suitable convex function H which captures the behavior at the origin of the dissipation. The present paper extends this analysis to nonlinear equations with viscoelasticity. It is shown that the decay rates of the energy are intrinsically described by the solution of the dissipative ODE St + c1H(c2S) = 0 with given intrinsic constants c1, c2 > 0. The results obtained are sharp and they improve (by introducing a novel methodology) previous results in the literature (see [6, 19-21]) with respect to (i) the criticality of the nonlinear exponent ρ and (ii) the generality of the relaxation kernel. [ABSTRACT FROM AUTHOR]

In the paper, the authors find two sharp and double inequalities for bounding the second Seiffert mean either by a one-parameter family of means derived from the centroidal mean or by a convex combination of the arithmetic and contra-harmonic means. [ABSTRACT FROM AUTHOR]

In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in | z | < 1, by using the hypergeometric function and the Owa–Srivastava operator Ωα defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365]. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a nondifferentiable multiobjective fractional programming problem (MFP) in which each component of objective functions contains the support function of a compact convex set. For a differentiable function, we introduce the class of second-order (C, α, ρ, d)-V-type-I convex functions. Further, Mond–Weir- and Wolfe-type duals are formulated for this problem and appropriate duality results are proved under the aforesaid assumptions. [ABSTRACT FROM AUTHOR]

For normalized starlike functions f : 픻 → ℂ, we consider the analytic functions g : 픻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part. [ABSTRACT FROM AUTHOR]

Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients. [ABSTRACT FROM AUTHOR]

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator. [ABSTRACT FROM AUTHOR]

In this paper we establish some related Ostrowski inequalities for the case of convex functions and general Lebesgue integral on measurable spaces. Midpoint and integral mean inequalities are provided, some particular results related to the famous Fejér's inequality are also given. [ABSTRACT FROM AUTHOR]

In this paper, we study abstract convexity topical and sub-topical functions. We obtain some results on abstract convexity such as support set and subdifferential in view of new elementary functions. Indeed, first we show that the ICR and IR functions are dense in IPH functions then the topical function and sub-topical function on topological vector space by another elementary function is studied. These elementary functions lead to obtain similar results with easier proofs. [ABSTRACT FROM AUTHOR]

Originally, partial information systems were introduced as a means of providing a representation of the Smyth powerdomain in terms of order convex substructures of an information-based structure. For every partial information system S, there is a new partial information system that is natrually induced by the principal lowersets of the consistency predicate for S. In this paper, we show that this new system serves as a completion of the parent system S in two ways. First, we demonstrate that the induced system relates to the parent system S in much the same way as the ideal completion of the consistency predicate for S relates to the consistency predicate itself. Second, we explore the relationship between this induced system and the notion of D-completions for posets. In particular, we show that this induced system has a "semi-universal" property in the category of partial information systems coupled with the preorder analog of Scott-continuous maps that is induced by the universal property of the D-completion of the principal lowersets of the consistency predicate for the parent system S. [ABSTRACT FROM AUTHOR]

Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a comprehensive study of operator m-convex functions.Let m ∈ [ 0 , 1 ] {m\in[0,1]} , and J = [ 0 , b ] {J=[0,b]} for some b ∈ ℝ {b\in\mathbb{R}} or J = [ 0 , ∞ ) {J=[0,\infty)}.A continuous function φ : J → ℝ {\varphi\colon J\to\mathbb{R}} is called operator m-convex if for any t ∈ [ 0 , 1 ] {t\in[0,1]} and any self-adjoint operators A , B ∈ 𝔹 ⁢ ( ℋ ) {A,B\in\mathbb{B}({\mathscr{H}})} , whose spectra are contained in J, we have φ ⁢ ( t ⁢ A + m ⁢ ( 1 - t ) ⁢ B ) ≤ t ⁢ φ ⁢ ( A ) + m ⁢ ( 1 - t ) ⁢ φ ⁢ ( B ) {\varphi(tA+m(1-t)B)\leq t\varphi(A)+m(1-t)\varphi(B)}.We first generalize the celebrated Jensen inequality for continuous m-convex functions and Hilbert space operators and then use suitable weight functions to give some weighted refinements.Introducing the notion of operator m-convexity, we extend the Choi–Davis–Jensen inequality for operator m-convex functions.We also present an operator version of the Jensen–Mercer inequality for m-convex functions and generalize this inequality for operator m-convex functions involving continuous fields of operators and unital fields of positive linear mappings.Employing the Jensen–Mercer operator inequality for operator m-convex functions, we construct the m-Jensen operator functional and obtain an upper bound for it. [ABSTRACT FROM AUTHOR]

In this paper, we establish Ostrowski-type inequalities for strongly convex functions, by using some classical inequalities and elementary analysis.We also give some results for the product of two strongly convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new dynamic inequalities on time scales whichas special cases contain several generalizations of integral and discreteinequalities due to Hardy, Copson, Leindler, Bennett, Pachpatte and Pečarić and Hanjš. [ABSTRACT FROM AUTHOR]

A mapping such that and is called a noncyclic mapping, where A and B are two nonempty subsets of a Banach space X. A best proximity pair for such a mapping T is a point such that and . In the current paper, we establish some existence results of best proximity pairs in strictly convex Banach spaces. The presented theorems improve and extend some recent results in the literature. We also obtain a generalized version of Markov-Kakutani's theorem for best proximity pairs in a strictly convex Banach space setting. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding a common solution of a Variational Inequality Problem (VIP) and the fixed point of quasi-nonexpansive mapping in a 2-uniformly convex and uniformly smooth Banach space. The TRSSEM does not require the computation of projection onto the feasible set of the VIP; instead, it uses a projection onto a finite intersection of sub-level sets of convex functions. The advantage of this is that any general convex feasible set can be involved in the VIP. We also introduce a modified TRSSEM which involves the projection onto the set of a convex combination of some convex functions. Under some mild conditions, we prove a strong convergence theorem for our algorithm and also present an application of our theorem to the approximation of a solution of nonlinear integral equations of Hammerstein's type. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our algorithm is simple and easy to implement for computation. [ABSTRACT FROM AUTHOR]

In this paper, we establish some Fejér-type inequalities for convex functions. They complement the results from the previous recent paper [DRAGOMIR, S. S.—MILOŠEVIĆ, D. S.—SÁNDOR, J.: On some refinements of Hadamard's inequalities and applications, Univ. Belgrad. Publ. Elek. Fak. Sci. Math. 4 (1993), 3-10]. [ABSTRACT FROM AUTHOR]

Let denote the usual class of all normalized functions harmonic and sense-preserving univalent on the unit disk . In this article we show that the set, consisting of those mappings f from for which all Taylor coefficients of the analytic and co-analytic parts of f are integers, consists of only nine functions. The second aim is to discuss the set of those functions which have half-integer coefficients. More precisely, we determine the set of univalent harmonic mappings with half-integer coefficients which are convex in real direction or convex in imaginary direction. This work generalizes the recent paper of Hiranuma and Sugawa. One of the examples generated in this way helps to disprove a conjecture of Bharanedhar and Ponnusamy. [ABSTRACT FROM AUTHOR]

Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected. [ABSTRACT FROM AUTHOR]

We generalize cyclic Jensen's inequality utilizing the theory of 4-convex function under the effect of introduced Green functions. We formulate result for power means and quasi means. Also we give applications in information theory by giving new estimations of generalized Csiszár divergence, Rényi-divergence, Shannon-entropy, Kullback-Leibler divergence and χ2-divergence. [ABSTRACT FROM AUTHOR]

The present paper investigates the projective bundles over small covers. We first give a necessary and sufficient condition for the projectivization of a real vector bundle over a small cover to be a small cover. Then associated with moment-angle manifolds, we further study the structure of such a projectivization as a small cover by introducing a new characteristic function on simple convex polytopes. As an application, we characterize the real projective bundles over 2-dimensional small covers by interpreting the fiber sum operation to some combinatorial operation. We next determine when the projectivization of Whitney sum of the tautological line bundle and the tangent bundle over real projective space is diffeomorphic to the product of two real projective spaces. This answers an open question regarding the topology of the fiber of the Monster-Semple tower. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new Ostrowski type inequalities for s-logarithmically convex functions. Some applications of our results to PDFs and in numerical integration are given. [ABSTRACT FROM AUTHOR]

A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained. [ABSTRACT FROM AUTHOR]

In this paper, some refinements of Hermite-Hadamard type inequalities for GA-convex functions are obtained. Applications of the obtained results to special means are given. [ABSTRACT FROM AUTHOR]

This paper considers the following problem: for what value r, r < 1 a function that is univalent in the unit disk |z| < 1 and convex in the disk |z| < r becomes starlike in |z| < 1. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered. [ABSTRACT FROM AUTHOR]

In this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space ℝn for any n ≥ 2. [ABSTRACT FROM AUTHOR]

In this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space ℝn for any n ≥ 2. [ABSTRACT FROM AUTHOR]