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We have established this paper on m convex functions, which can be expressed as a general form of the convex function concept. First of all, some inequalities of Hadamard type are proved with fairly simple conditions. Next, an integral identity containing Atangana-Baleanu fractional integral operators is obtained to prove new inequalities for differentiable m-convex functions. Using this identity, various properties of m convex functions and classical inequalities, some new integral inequalities have been proved. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [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 the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems. [ABSTRACT FROM AUTHOR]

In the paper we discuss two functionals of the Fekete-Szegö type: Φf(µ) = a2a4 -- µ,a3² and ©/(µ) = a4 -- µa2a3 for an analytic function f (z) = z + a2z² + a3z³ + . . ., z € Δ, (Δ = {z € C : |z| < 1}) and a real number µ. We focus our research on the estimation of (µ)| and \©f (µ)|, while f is either in S* (the class of starlike functions) or in Κ (the class of convex functions). [ABSTRACT FROM AUTHOR]

In the present paper, we investigate upper bounds on the third Hankel determinants for the starlike and convex functions with respect to symmetric points in the open unit disk. [ABSTRACT FROM AUTHOR]

We study semi-convex frontier (SCF) optimization problems where objective functions can be semi-convex and constraint sets can be non-polyhedron, which stem from a growing range of optimization applications such as frontier analysis, multi-objective programming in economics. The new findings of this paper can be summarized as follows: (1) We characterize non-dominated points of a non-polyhedron optimal solution set of a semi-convex frontier program. (2) We obtain optimality conditions of a constant modulus SCF program, of which the objective function is semi-convex with a constant semiconvexity modulus. (3) We obtain a non-smooth Hölder stability of the optimal solutions of a semiconvex frontier program. (4) We use generalized differentiability to establish sensitivity analysis of the optimal value function of a semi-convex frontier program. [ABSTRACT FROM AUTHOR]

In this paper we investigate continuity properties of functions $${f : \mathbb {R}_+ \to \mathbb {R}_+}$$ that satisfy the ( p, q)-Jensen convexity inequality where H stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are ( p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is ( p, p)-Jensen convex for all $${p \in P \subseteq \mathbb {R}_+}$$ , where P is a set of positive Lebesgue measure, then f must be continuous. [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]

In this paper, we consider a new class 풞(ϕ, ψ, η) of analytic functions defined by means of subordination. Coefficient bounds, Fekete-Szegö problem and norm estimates of the pre-Schwarzian derivatives of functions belonging to the class 풞(ϕ, ψ, η) are investigated. A class of multiple close-to-convex functions is also considered. [ABSTRACT FROM AUTHOR]