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Inspired by the idea and technique in a recent paper of Huy et al. (Linear Algebra Appl 656: 368–384, 2023), Ighachane and Bouchangour showed an important refinement of the results by Sababheh (Linear Algebra Appl 506: 588–602, 2016) involving both convex and log-convex functions. In this paper, we continue to establish further new inequalities for both convex and log-convex functions with some applications to scalar and matrix means as well as matrix norm and numerical radius. The significance of the obtained results is two folded: the results themselves and the way they extend many known results in the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided. [ABSTRACT FROM AUTHOR]

In this paper, some concepts of convex analysis on hyperbolic spaces are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex sets and the intrinsic projection onto these sets. We also study the concept of convex functions and present first- and second-order characterizations of these functions, as well as some optimization concepts related to them. An extensive study of the hyperbolically convex quadratic functions is also presented. [ABSTRACT FROM AUTHOR]

Cotîrlă and Szász (Comput Methods Funct Theory: 2023) solved a conjecture related with inclusion relation for Bessel functions, proposed by Baricz and András (Complex Var Elliptic Equ 54(7): 689–696, 2009). In this paper, we prove this conjecture for normalized Struve functions by using subordination factor sequences. [ABSTRACT FROM AUTHOR]

The authors of (Complex Var Elliptic Equ 54(7):689–696, 2009) proved a kind of monotony of Bessel functions using integral represen- tations. This paper establishes a monotonicity property for the normalized Lommel function of the first kind using the method of subordination factor sequences. [ABSTRACT FROM AUTHOR]

We formulate Hermite–Hadamard–Mercer type inequalities for ( A B K -FI) (Atangana–Baleanu Katagampula Fractional Integral) operators. We present new Dragomir–Agarwal type identities and establish a variants of Jensen–Hermite–Hadamard type inequalities involving A B K -FI operators for differentiable convex mappings. We present new bounds by employing Young and Hölder inequalities. We make links between our findings and a number of well-known discoveries in the literature. Finally, to support the effectiveness of our obtain results, we expose some inequalities examples in terms of Modified Bessel functions and matrices. The findings of this paper may lead to more research in this field. [ABSTRACT FROM AUTHOR]

In this paper, we establish several new inequalities for q-differentiable coordinated convex functions that are related to the right side of Hermite–Hadamard inequalities for coordinated convex functions. We also show that the inequalities proved in this paper generalize the results given in earlier works. Moreover, we give some examples in order to demonstrate our main results. [ABSTRACT FROM AUTHOR]

This paper proves an equality for the case of differentiable convex functions including the conformable fractional integrals. By using this equality, we establish several parameterized inequalities with the help of the conformable fractional integrals. Several inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems. [ABSTRACT FROM AUTHOR]

In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification and the modified Abadie constraint qualification, the Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization problems by using the nonlinear version Gordan theorem of the alternative for convex functions. Further, the sufficient optimality conditions for such directionally differentiable multiobjective programming problems with vanishing constraints are proved under convexity hypotheses. Furthermore, vector Wolfe dual problem is defined for the considered directionally differentiable multiobjective programming problem vanishing constraints and several duality theorems are established also under appropriate convexity hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an equality involving tempered fractional integrals for twice-differentiable functions. By using this equality, we establish several left Hermite–Hadamard-type inequalities for the case of tempered fractional integrals. Moreover, we derive our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

In this paper, versions of the famous Jensen inequality for sublinear isotonic functionals are proved. The obtained results generalize classic Jessen's and McShane's inequalities. Applications to generalized means and to Hölder's and Minkowski's inequalities are also given. [ABSTRACT FROM AUTHOR]

In this paper, new inequalities for the left and right sides of the Hermite–Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems. [ABSTRACT FROM AUTHOR]

In this paper we present a subgradient method with non-monotone line search for the minimization of convex functions with simple convex constraints. Different from the standard subgradient method with prefixed step sizes, the new method selects the step sizes in an adaptive way. Under mild conditions asymptotic convergence results and iteration-complexity bounds are obtained. Preliminary numerical results illustrate the relative efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate uniform decay estimate of the solution to the Petrovsky equation with memory u tt + Δ 2 u - ∫ 0 t g (t - s) Δ 2 u (s) d s = 0 with initial conditions and boundary conditions, where g is a memory kernel function. The related energy has been shown to decay exponentially or polynomially as t → + ∞ by the theorem established under the assumption g ′ (t) ⩽ - k g 1 + 1 p (t) with p ∈ (2 , ∞) and k > 0 in the reference(J Funct Anal 254(5):1342–1372, 2008). Using the ideas introduced by by Lasiecka and Wang (Springer INdAM Series 10, Chapter, vol 14, pp 271–303, 2014), we prove the optimized uniform general decay result under the assumption g ′ (t) + H (g (t)) ≤ 0 , where the function H (·) ∈ C 1 (R 1) is positive, increasing and convex with H (0) = 0 , which is introduced for the first time by Alabau-Boussouira and Cannarsa (C R Acad Sci Paris Ser I 347:867–872, 2009) and studied systematically by Lasiecka and Wang (Springer INdAM Series 10, Chapter, vol 14, pp 271–303, 2014). The exponential decay result and polynomial decay result in the reference (J Funct Anal 254(5):1342–1372, 2008) are the special cases of this paper by choosing special H (·) . [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present some new properties of convex functions, including Mercer-type, superadditive-type, and Jensen-type inequalities. Applications of these new properties will cover the celebrated Hermite–Hadamard inequality, Clarkson inequality, and the operator Mercer inequality. Comparisons with some existing results will be discussed too. [ABSTRACT FROM AUTHOR]

In this paper, some concepts related to the intrinsic convexity of non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in the Euclidean space, the study of intrinsic convexity of non-homogeneous quadratic functions in the hyperbolic space is more elaborate than that of homogeneous quadratic functions. Several characterizations that allow the construction of many examples will be presented. [ABSTRACT FROM AUTHOR]

In this paper, the exact minimax penalty function method is applied to solve constrained multiobjective optimization problems involving locally Lipschitz functions. The criteria for a saddle point for the original vector optimization problem are studied with the help of the penalized unconstrained vector optimization problem. Furthermore, we determine the conditions for which the (weak) efficient solutions of the vector optimization problem are equivalent to those of the associated, penalized unconstrained vector optimization problem. Some examples of nonsmooth multiobjective problems solved by using the exact minimax penalty method are presented to illustrate the results established in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by applying the notion of q b -integral. We prove some new inequalities related with right-hand sides of q b -Hermite–Hadamard inequalities for differentiable functions with convex absolute values of second derivatives. The results presented in this paper are a unification and generalization of the comparable results in the literature on Hermite–Hadamard inequalities. [ABSTRACT FROM AUTHOR]

Integral operators have a very vital role in diverse fields of science and engineering. In this paper, we use φ-convex functions for unified integral operators to obtain their upper bounds and upper and lower bounds for symmetric φ-convex functions in the form of a Hadamard inequality. Also, for φ-convex functions, we obtain bounds of different known fractional and conformable fractional integrals. The results of this paper are applicable to convex functions. [ABSTRACT FROM AUTHOR]

This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroşanu (Optim Lett 7:415–420, 2013) is discussed. Noticing the inappropriate formulation of that algorithm, we propose a more general algorithm for approximating zeros of a maximal monotone operator on a Hilbert space. Besides the main result on the strong convergence of the sequences generated by this new algorithm, we discuss some particular cases, including the approximation of minimizers of convex functionals and present two examples to illustrate the applicability of the algorithm. The note clarifies and extends both the papers quoted above. [ABSTRACT FROM AUTHOR]

In this paper, we consider a viscoelastic von Karman equation with damping, delay, and source effects of variable exponent type. Firstly, we show the global existence of solution applying the potential well method. Then, by making use of the perturbed energy method and properties of convex functions, we derive general decay results for the solution under more general conditions of a relaxation function. General decay results of solutions for viscoelastic von Karman equations with variable exponent nonlinearities have not been discussed before. Our results extend and complement many results for von Karman equations in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider coefficient estimates in a class of functions consisting of analytic functions normalized by in the open unit disk subordinating with nephroid domain, to derive certain coefficient estimates and Fekete–Szegő inequality for . A similar result have been done for the function Further application of our results to certain functions defined by convolution products with a normalized analytic function is given, and in particular we obtain Fekete–Szegő inequalities for certain subclasses of functions defined through neutrosophic Poisson distribution. [ABSTRACT FROM AUTHOR]

Fractional calculus operators play a very important role in generalizing concepts of calculus used in diverse fields of science. In this paper, we use Riemann–Liouville fractional integrals to establish generalized identities, which are further applied to obtain midpoint and trapezoidal inequalities for convex function with respect to a strictly monotone function. These inequalities reproduce midpoint and trapezoidal inequalities for convex, harmonic convex, p-convex, and geometrically convex functions. Also, some new inequalities can be generated via specific strictly monotone functions. [ABSTRACT FROM AUTHOR]

In this paper, under the generalized assumptions of the memory kernel function, using the idea introduced by Lasiecka and Wang (Intrinsic decay rate estimates for semilinear abstract second order equations with memory. Springer INdAM Series 10, New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Chap. 14, Springer, Switzerland, 2014) we prove the general decay result to an initial boundary value problem of a wave equation with variable density. Our general assumptions of the memory kernel function generalize the assumptions in the literature (Alabau-Boussouira et al. in J Funct Anal 254(5):1342–1372, 2008; Messaoudi and Khulaifi in Appl Math Lett 66:16–22, 2017). [ABSTRACT FROM AUTHOR]

In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions. [ABSTRACT FROM AUTHOR]

The main target of this paper is to discuss operator Hermite–Hadamard inequality for convex functions, without appealing to operator convexity. Several forms of this inequality will be presented and some applications including norm and mean inequalities will be shown too. [ABSTRACT FROM AUTHOR]

Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean inequality. [ABSTRACT FROM AUTHOR]

This paper proposes three enlargements of the conventional Moreau–Rockafellar subdifferential: the sup-, sup⋆- and symmetric subdifferentials. They satisfy the most fundamental properties of the conventional subdifferential: convexity, weak∗-closedness and, if the function is bounded, weak∗-compactness. Moreover, they are nonempty for the Rainwater function, possess certain calculus rules, and provide necessary and sufficient optimality conditions for not necessarily convex functions. [ABSTRACT FROM AUTHOR]

Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, Burachik and Martínez-Legaz showed that the well-known Bregman distance is a particular case of a general family of distances, each one induced by a specific maximally monotone operator and a specific choice of one of its representative functions. For the family of generalized Bregman distances, sufficient conditions for convexity, coercivity, and supercoercivity have recently been furnished. Motivated by these advances, we introduce in the present paper the generalized left and right envelopes and proximity operators, and we provide asymptotic results for parameters. Certain results extend readily from the more specific Bregman context, while others only extend for certain generalized cases. To illustrate, we construct examples from the Bregman generalizing case, together with the natural "extreme" cases that highlight the importance of which generalized Bregman distance is chosen. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new refinement of the left-hand side of Hermite-Hadamard inequality for convex functions of several variables defined on simplices. [ABSTRACT FROM AUTHOR]

In this paper, we first show that for a Banach space X there is a fully order-reversing mapping T from conv(X) (the cone of all extended real-valued lower semicontinuous proper convex functions defined on X) onto itself if and only if X is reflexive and linearly isomorphic to its dual X*. Then we further prove the following generalized Artstein-Avidan-Milman representation theorem: For every fully order-reversing mapping T: conv(X) → conv(X) there exist a linear isomorphism U: X → X*, x0*, φ0 ∈ X*, α > 0 and r0 ∈ ℝ so that (T f) (x) = α (ℱ f) (U x + x 0 ∗) + 〈 φ 0 , x 〉 + r 0 , ∀ x ∈ X , where ℱ : conv(X) → conv(X*) is the Fenchel transform. Hence, these resolve two open questions. We also show several representation theorems of fully order-preserving mappings defined on certain cones of convex functions. For example, for every fully order-preserving mapping S: semn(X) → semn(X) there is a linear isomorphism U: X → X so that (S f) (x) = f (U x) , ∀ f ∈ semn (X) , ∀ x ∈ X , where semn(X) is the cone of all lower semicontinuous seminorms on X. [ABSTRACT FROM AUTHOR]

The Baillon–Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is β -Lipschitz if and only if it is 1 / β -cocoercive. In this paper, we extend this theorem to Gâteaux differentiable and lower semicontinuous convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of C 1 , + convex functions in terms of local cocoercivity. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a bilevel optimization problem P0, where the lower level problem is a vector optimization problem. First, we give an equivalent one level optimization problem for which the nonsmooth Mangasarian–Fromowitz constraint qualification can hold at feasible solution. Using a special scalarization function, one deduces necessary optimality condition for the initial problem. [ABSTRACT FROM AUTHOR]

In this paper, the standard Jensen inequality for two points and convex functions is generalized to a version for four points satisfying Sherman's majorization condition and for G-invariant convex functions, where G is a subgroup of the orthogonal group acting on an inner product space. A control map is used. A comparison of the obtained inequality and Jensen inequality is presented. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problem on the description in terms of the Laplace transform of functionals from the conjugate space for the Hilbert space of entire functions of n variables constructed by a convex function in ℂn, which depends on the modules of variables and grows at infinity faster than a‖z‖ for any a > 0. [ABSTRACT FROM AUTHOR]

In this paper, we present some inequalities for Csiszár f-divergence between two probability measures on time scale. These results extend some known results in the literature and offer new results in h-discrete calculus and quantum calculus. We also present several inequalities for divergence measures. [ABSTRACT FROM AUTHOR]

In this paper, a preorder relation for Schur-convex functions on R n is introduced. A majorization statement is shown for the gradients and divergences of two Gateaux differentiable Schur-convex functions, provided that the difference of the involved functions is also Schur-convex. This implies the monotonicity of a related operator with respect to the used preorder and the classical majorization preorder on R n . Special cases of the main result are also studied. In particular, applications are given for strongly convex functions. Some comparisons of variances are presented for uniform distribution. [ABSTRACT FROM AUTHOR]

In this paper, we give new singular value inequalities for matrices. It is shown that if A, B, X are n × n matrices such that X is positive semidefinite, and if f : [ 0 , ∞) → R is an increasing nonnegative convex function, then s j f A X B ∗ X ≤ f A ∗ A + B ∗ B 2 X s j X and s j A X B ∗ ≤ 1 2 A ∗ A A 2 + B ∗ B B 2 A B s j X for j = 1 , 2 ,... , n . Some of our inequalities present refinements of some known singular value inequalities. [ABSTRACT FROM AUTHOR]

This paper studies fractional integral inequalities for fractional integral operators containing extended Mittag-Leffler (ML) functions. These inequalities provide upper bounds of left- and right-sided fractional integrals for (α , h − m) convex functions. A generalized fractional Hadamard inequality is established. All the results hold for h-convex, (h , m) -convex, (α , m) -convex, (s , m) -convex, and associated functions. [ABSTRACT FROM AUTHOR]

In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory. [ABSTRACT FROM AUTHOR]

This part of the paper analyzes new properties of cuts in undirected graphs, presents various models for the maximum cut problem, based on the established correspondence between the cuts in this graph and the specific bases of the extended polymatroid associated with this graph. With respect to the model, formulated as maximization of the convex function on the compact set (extended polymatroid), it was proved that the objective function has the same value at any local and global maxima, i.e., to solve the maximum cut problem, it will suffice to find a base of the extended polymatroid as a local or global maximum of the objective function. [ABSTRACT FROM AUTHOR]

The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen's inequality in time scales settings. The concept of differential entropy of a continuous random variable on time scales is introduced, and its bounds for some particular distributions are also estimated. [ABSTRACT FROM AUTHOR]

In this paper we have derived the fractional integral inequalities by defining exponentially (s , m) -convex functions. These inequalities provide upper bounds, boundedness, continuity, and Hadamard type inequality for fractional integrals containing an extended Mittag-Leffler function. The results about fractional integral operators for s-convex, m-convex, (s , m) -convex, exponentially convex, exponentially s-convex, and convex functions are direct consequences of presented results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also it isometrically splits a line. We have also proved that a gradient Ricci soliton with non-constant concave potential function and bounded Ricci curvature is non-shrinking and hence the scalar curvature has at most one critical point. [ABSTRACT FROM AUTHOR]

Let F be the class of functions f (z) = z + a 2 z 2 + ⋯ which are analytic in D = { z : | z | < 1 } and satisfies the condition 1 + 1 b z f ′ ′ (z) f ′ (z) = p t (z) , (b ≠ 0 , b ∈ C , z ∈ D) where p t (z) = t 4 + 1 2 p 1 (z) - t 4 - 1 2 p 2 (z) , t ≥ 2 , p 1 (z) , p 2 (z) ∈ P . P is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by K(t, b). In this present paper, we will introduce this class and its some properties. [ABSTRACT FROM AUTHOR]

In this paper, the class of weakly ψ -uniformly convex functions is introduced and studied. Such functions are defined on a convex subcone D of a linear space V endowed with the structure of a normal decomposition system (V , G , (·) ↓) . In particular, superquadratic functions and c-strongly convex functions are recovered as special cases. Some results in Abramovich et al. (J Math Anal Appl 327: 1444–1460, 2007), intended for multidimensional superquadratic functions defined on R + m , are extended to the case of weakly ψ -uniformly convex functions. The concept of ψ -almost superadditivity of functions is presented and applied. Interpretations of the obtained results are demonstrated for some matrix normal decomposition systems. [ABSTRACT FROM AUTHOR]

The paper gives answer to two open questions related to Mulholland's inequality. First, it is shown that there exists a larger set of solutions to Mulholland's inequality compared to the one delimited by Mulholland's condition. Second, it is demonstrated that the set of functions solving Mulholland's inequality is not closed with respect to compositions. [ABSTRACT FROM AUTHOR]