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This paper deals with the class S containing functions which are analytic and univalent in the open unit disc U = {z ∈ C: |z| < 1}. Functions f in S are normalized by f(0) = 0 and f′(0) = 1 and has the Taylor series expansion of the form f(z) = z + ∞X n=2 anzn. In this paper we investigate on the subclass of S of close-to-convex functions denoted as Cgα(λ, δ) where function f ∈ Cgα(λ, δ) satisfies Re{eiλ zf′(z) gα(z) } for |λ| < π 2, cos(λ) > δ, 0 ≤ δ < 1, 0 ≤ α ≤ 1 and gα = z (1-αz)2. The aim of the present paper is to find the upper bound of the Fekete-Szego functional |a3 - μa2 2| for the class Cgα(λ, δ). The results obtained in this paper is significant in the sense that it can be used in future research in this field, particularly in solving coefficient inequalities such as the Hankel determinant problems and also the Fekete-Szego problems for other subclasses of univalent functions. [ABSTRACT FROM AUTHOR]

In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for the case of quasi-arithmetically convex (q-ac) functions which acts as a generator for all quasi-arithmetic means in the frame work of Sugeno integral. [ABSTRACT FROM AUTHOR]

In 2013, Azadifar et al. [3] established fixed point result in integral type contraction in modular metric space and 2020, Chaira et al.[11] established some extensions of Fixed Point Theorems for Weak-Contraction Mapping in Partially Ordered Modular Metric Spaces. In this paper we have established some common fixed point results in integral type contractions in modular and convex modular metric spaces. [ABSTRACT FROM AUTHOR]

Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the convexity preserving properties of sets by direct and inverse images initially stated for set-valued ratios of affine functions to a broader class of fractional type set-valued functions which strictly includes the first one. [ABSTRACT FROM AUTHOR]

We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas. [ABSTRACT FROM AUTHOR]

We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown. [ABSTRACT FROM AUTHOR]

In this paper, we look at the general form of the two-point quadrature formulas, which doesn't have to be symmetric. Under the convexity constraint of the first derivative, we propose a new scheme that gives the best approximation of the two-point quadrature rules. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to find a necessary and sufficient condition for Miller-Ross-type Poisson distribution series to be in the class 풲δ(α, γ, β) of analytic functions with negative coefficients.Also, we investigate several inclusion properties of the classes 풮∗, 풦 and ℝτ(A, B) associated of the operator 핀ν,cm defined by this distribution. Further, we consider an integral operator related to Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of pre-Schur convex functions defined on general domains from plane. Then, by making use of Green's identity for double integrals, we establish some integral inequalities for this class of functions that naturally generalize the case of Schur convex functions. Some exmples for rectangles and disks are also provided. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with q-derivative. We also study certain a convolution conditions, and apply the convolution conditions to get sufficient condition and the neighborhood results related to the functions in the class 풮q(A, B, α). [ABSTRACT FROM AUTHOR]

This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties. The main idea of the proposed method is to develop a robust closed-loop controller based on sliding modes where the sliding surface takes the trajectory around a zone of the optimal point. We assume that the output of the plant is given by the states and a measure of the function. We show the stability and zone-convergence of the proposed algorithm. In order to validate the proposed method, we present a numerical example. [ABSTRACT FROM AUTHOR]

This paper is concerned with certain generalized subclasses of multivalent quasi-convex functions defined with subordination. Various properties of these classes in regard to the coefficient estimates, distortion theorems, growth theorems, argument theorems and inclusion relations are discussed. Also, the relations with the earlier known results are established. [ABSTRACT FROM AUTHOR]

In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized convex functions called (h, r)-preinvex functions, and establish some new Hermite-Hadamard type inequalities under (h, r)-preinvexity. [ABSTRACT FROM AUTHOR]

In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fej'er's inequality for convex functions and of Gr¨uss' type inequalities are also provided. [ABSTRACT FROM AUTHOR]

In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients ja2j and ja3j for the functions in these classes. Also we investigate upper bounds for the Fekete-Szego functional and second Hankel determinant for these classes. [ABSTRACT FROM AUTHOR]

Balaban index is defined as J(G) = m /m-n+2 ... 1/√w(u) ⋅ w(v), where the sum is taken over all edges of a connected graph G, n and m are the cardinalities of the vertex and the edge set of G, respectively, and w(u) (resp. w(v)) denotes the sum of distances from u (resp. v) to all the other vertices of G. In 2011, H. Deng found an interesting property that Balaban index is a convex function in double stars. We show that this holds surprisingly to general graphs by proving that attaching leaves at two vertices in a graph yields a new convexity property of Balaban index. We demonstrate this property by finding, for each n, seven trees with the maximum value of Balaban index, and we conclude the paper with an interesting conjecture. [ABSTRACT FROM AUTHOR]

In this paper, for a semi-infinite optimization Problem (P), second order - approximated optimization problems (P0,2), (P2,0), (P1,2), (P2,1) and (P2,2) are constructed. Some connections are established between the optimal solutions of these problems and optimal solutions of the original Problem (P). [ABSTRACT FROM AUTHOR]

The theory and applications of dynamic derivatives on time scales have recently received considerable interest. In this paper, we define a function using the combined diamond-α integral, investigate its monotonicity and give some refinements for Hölder's inequality. We present some applications for ℤ and ℝ. [ABSTRACT FROM AUTHOR]

Motivated by the Szostok problem on functions with monotonic differences (2005, 2007), we consider a-Wright convex functions as a generalization of Wright convex functions. An application of these results to obtain new proofs of known results as well as new results is presented. [ABSTRACT FROM AUTHOR]

In this paper, is defined the operator Dλ,ν,nα,β : A → A, given by Dλ,ν,nα,β f(z) = (1 - α - β)RνDnf(z) + αRνΩλzf(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλz is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2z² + a3z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,nα,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,nα,β (δ) and some differential subordinations using the operator Dλ,ν,nα,β. [ABSTRACT FROM AUTHOR]

In this paper we give a new generalized and sharpend version of Aczél- Popoviciu inequality via positive and homogeneous functionals. [ABSTRACT FROM AUTHOR]

In this paper we establish some new general integral inequalities for twice differentiable functions. Then we apply these inequalities to obtain some inequalities for special means of real numbers. Finally, some new general quadrature rules of trapezoidal type are provided. [ABSTRACT FROM AUTHOR]

In this paper, we prove that Bernstein type Cheney and Sharma operators preserve modulus of continuity and Lipschitz continuity properties of the attached function f. We also introduce a result for these operators when f is a convex function. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class L(λ, μ, ϕ) of analytic functions f dened in the open unit disk U satisfying the subordination condition that q(z) Dλ+1f(z)/Dλf(z) ≺ ϕ(z) (λ ∈ N0; μ ≥ 0; z ∈ U); where q(z) = (z/Dλf(z))μ-2, Dλ is the Sλalλagean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coeficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f(z), sharp bounds for the initial coeficient and for the Fekete-Szego functional are determined, and also some integral representations are given. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a new subclass χtp(γ) of analytic and p-valent close-to-convex functions in the open unit disk U. For functions belonging to the class χtp(γ), some interesting properties including the coefficient estimates, distortion theorems and subordination results are obtained. [ABSTRACT FROM AUTHOR]

In the present paper, we find certain results on Ruscheweyh operator using differential inequality. In particular, we find sufficient conditions for starlike and convex functions. [ABSTRACT FROM AUTHOR]

For a continuous and positive function w (λ) , λ > 0 and µ a positive measure on (0, ∞) we consider the following integral transform 풟 (w , μ) (T) : = ∫ 0 ∞ w (λ) (λ + T) - 1 d μ (λ) , where the integral is assumed to exist for T a positive operator on a complex Hilbert space H. Assume that A ≥ α > 0, δ ≥ B > 0 and 0 < m ≤ B − A ≤ M for some constants α, δ, m, M. Then 0 ≤ - m 풟 ′ (w , μ) (δ) ≤ 풟 (w , μ) (A) - 풟 (w , μ) (B) ≤ - M 풟 ′ (w , μ) (α) , where D′(w, µ) (t) is the derivative of D(w, µ) (t) as a function of t > 0. If f : [0, ∞) → ℝ is operator monotone on [0, ∞) with f (0) = 0, then 0 ≤ m δ 2 [ f (δ) - f ′ (δ) δ ≤ f (A) A - 1 - f (B) B - 1 ] ≤ M α 2 [ f (α) - f ′ (α) α ]. Some examples for operator convex functions as well as for integral transforms D (·, ·) related to the exponential and logarithmic functions are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms. We give some Hermite-Hadamard type inequalities for convex, harmonically convex and p-convex functions. Some results presented in this paper for p-convex functions, provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

In this article we present a method to get upper bound for some integrals. The method is in connection with on a generalized trapezoidal quadrature formula. Applications for upper bounds of the elliptical integral of the first kind are presented. We compare these bounds with some previous results from the literature. [ABSTRACT FROM AUTHOR]

We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2 gain analysis problem for the switched affine time-varying systems under state feedback. [ABSTRACT FROM AUTHOR]

In this paper, the author establishes a new identity for differentiable func-tions and obtain some new inequalities for differentiable functions based on s-convexity, m-convexity and (,m)-convexity via Riemann-Liouville fractional integrals involving Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper, we derive sufficient conditions for the univalence, starlikeness, convexity and some other properties in the class N (ρ), for a new integral operator defined on the space of normalized analytic functions in the open unit disk. [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 purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk 𝔻. Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

The aim of this paper is to extend a result presented by Roman Ger during the 15th International Conference on Functional Equations and Inequalities. First, we present some necessary and sufficient conditions for a continuous function to be convex. We will use these to extend Ger’s result. Finally, we make some connections with other mathematical notions, as g-convex dominated function or Bregman distance.

In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.

In this paper we have introduced and studied the subclass ℛ𝒥 (d, α, β) of univalent functions defined by the linear operator RIn,λ,lγf(z)$RI_{n,\lambda ,l}^\gamma f(z)$ defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n, λ, l) f(z), as RIn,λ,lγ:𝒜→𝒜$RI_{n,\lambda ,l}^\gamma :{\cal A} \to {\cal A}$, RIn,λ,lγf(z)=(1−γ)Rnf(z)+γI(n,λ,l)f(z)$RI_{n,\lambda ,l}^\gamma f(z) = (1 - \gamma )R^n f(z) + \gamma I(n,\lambda ,l)f(z)$, z ∈ U, where 𝒜n ={f ∈ 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 ℛ𝒥(d, α, β).

Extension of Montgomery's identity is used in derivation of Popoviciu-type inequalities containing sums..., where f is an n-convex function. Integral analogues and some related results for n-convex functions at a point are also given, as well as Ostrowski-type bounds for the integral remainders of identities associated with the obtained inequalities. [ABSTRACT FROM AUTHOR]

Non-parametric density estimation with shape restrictions has witnessed a great deal of attention recently. We consider the maximum- likelihood problem of estimating a log-concave density from a given finite set of empirical data and present a computational approach to the resulting optimization problem. Our approach targets the ability to trade-off computational costs against estimation accuracy in order to alleviate the curse of dimensionality of density estimation in higher dimensions. [ABSTRACT FROM AUTHOR]