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In this paper, we report on some recent results obtained in our joint paper Papageorgiou and Rădulescu (2015). We consider a Robin problem driven by a nonhomogeneous differential operator and with a reaction that exhibits competing effects of concave (that is, sublinear) and convex (that is, superlinear) nonlinearities. Without employing the Ambrosetti–Rabinowitz condition, we establish a bifurcation property of the positive solutions near the origin. The approach relies on variational methods and elliptic estimates. [ABSTRACT FROM AUTHOR]

Summation inequalities method for quadratic functions plays a key role in the field of stability analysis, in which the information of time-varying delay and states can be introduced. Generally, the information of delay variation is introduced by the forward difference of Lyapunov–Krasovskii functional, which may lead to some underutilized delay information due to its internal constraints. This paper proposes a new summation inequality for quadratic functions by defining a set of convex functions, which simultaneously introduces the delay amplitude and variation in a summation inequality. A delay amplitude and variation-dependent stability criterion is obtained by using the summation inequality. A numerical example is given to substantiate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce and investigate various inclusion relationships and convolution properties of a certain class of meromorphically p-valent functions, which are defined in this paper by means of a linear operator. [Copyright &y& Elsevier]

This paper is devoted to a rigorous analysis of one dimensional Particle Swarm Optimization (PSO) for non convex objective function. We provide a quantitative bound on the error between the equilibrium point and the global minimizer of the given objective function. Our strategy does not rely on the Laplace principle. We also investigate the underdamped PSO with linear objective function. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the energy decay rates for the viscoelastic wave equation with acoustic boundary conditions. Here we consider with minimal conditions on the L 1 (0 , ∞) relaxation function α , namely α ′ (t) ≤ − ζ (t) G (α (t)) , where G is an increasing and convex function near the origin and ζ is a nonincreasing function. Using the assumptions on the relaxation function α due to Mustafa (2018), we generalize the work of Park and Park (2011) and Liu (2014) to general decay. [ABSTRACT FROM AUTHOR]

In this paper, we study continuous properties of adapted solutions for backward stochastic differential equations with constraints (CBSDEs in short). Comparing with many existing literatures about this topic, our case is very general in the sense that constraints are formulated by general non-negative real functions. In general case, we proved a continuous property from below and a lower semi-continuous property of the minimal super-solution of CBSDE in its effective domain. Furthermore, in the special convex case, we obtained a continuous property with the help of convex analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with a von Karman equation with memory and time-varying delay. For a more general type of relaxation function β , we prove the general decay results. This work generalizes and improves previous results for the von Karman equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the multiplicity of solutions for the nonhomogeneous -Kirchhoff elliptic equation with zero Dirichlet boundary condition on , where is the complement of a smooth bounded domain in . , , and are continuous functions which may change sign on . The parameters satisfy . A new existence result for multiple solutions is obtained by the Mountain Pass Theorem and Ekeland’s variational principle. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity are derived. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce two new subclasses of the function class of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients and for functions in these new subclasses. [Copyright &y& Elsevier]

Abstract: This paper deals with some basic notions of convex analysis and convex optimization via convex semi-closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex sub-differential sum rule and two separation results. Finally, the derived convex sub-differential sum rule is applied to solving the convex programming problem. [Copyright &y& Elsevier]

Abstract: The harmonic function in the open unit disc can be written as a sum of an analytic and an anti-analytic function, , where and are analytic functions in , and are called the analytic part and co-analytic part of , respectively. One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion), because the growth theorem and distortion theorem give the compactness of the classes of these functions. In this paper we consider both of these questions with the shear construction method. [Copyright &y& Elsevier]

Abstract: In this paper, we find the necessary and sufficient conditions for functions in the generalized class of uniformly starlike and uniformly convex functions of order and also consequences of the results are pointed out. [Copyright &y& Elsevier]

Abstract: In the present paper, we introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk whose inverse has univalently analytic continuation to . Among other results, bounds for the Taylor–Maclaurin coefficients and are found in our investigation. [Copyright &y& Elsevier]

Abstract: In this paper, a class of time delay systems with nonlinear uncertainties is considered. A novel robust stability criterion of the system is derived by using the Lyapunov method. The criterion can be easily solved by efficient convex optimization algorithms. Two numerical examples are given to illustrate the superiority of our result to those in the literature. [Copyright &y& Elsevier]

Abstract: An interesting criterion was given by Ponnusamy and Singh [S. Ponnusamy, V. Singh, Convolution properties of some classes of analytic functions, Internal Report, SPIC Science Foundation, 1990.] for convolution properties of functions in the class . In this paper we shall get a new criterion for convolution properties of functions in this class. [Copyright &y& Elsevier]

In this paper, we shall introduce two new inequalities of Hermite-Hadamard type for convex functions with bounded derivatives. Some applications to special means of real numbers are also included. [Copyright &y& Elsevier]

In this paper, we present necessary and sufficient conditions of efficiency and weak efficiency under generalized cone-convexity and cone-subconvexity. The results are stated in partially ordered real linear spaces from a separation theorem between convex cones which need not be solid. [Copyright &y& Elsevier]

In this paper, we discuss the k -convex solution to the following boundary blow-up k -Hessian equation with singular weights: S k D 2 u = H (x) u p , in Ω , u = ∞ , on ∂ Ω , where k ∈ { 1 , 2 , ... , n } , S k D 2 u is the k -Hessian operator, Ω is a smooth, bounded and strictly convex domain in R n (n ≥ 2) , p > 0. [ABSTRACT FROM AUTHOR]