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This research paper investigated weighted Milne-type inequalities utilizing Riemann-Liouville fractional integrals across diverse function classes. A key contribution lies in the establishment of a fundamental integral equality, facilitated by the use of a nonnegative weighted function, which is pivotal for deriving the main results. The paper systematically proved weighted Milne-type inequalities for various function classes, including differentiable convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation. The obtained results not only contribute to the understanding of Milne-type inequalities but also offer insights that pave the way for potential future research in the considered topics. Furthermore, it is evident that the results obtained encompass numerous findings that were previously presented in various studies as special cases. [ABSTRACT FROM AUTHOR]

In this paper, using the results of a recent paper by the author, we give a new method for proving refinements of inequalities related to convex functions on intervals. In many cases, the proof is simpler and more transparent than using the usual techniques, and the essence of the refinement is clearer. This is illustrated by two refinements of the Jensen’s inequality and one refinement of the Lah-Ribarič inequality. As an application we generalize a recent result for strongly convex functions. [ABSTRACT FROM AUTHOR]

In the present paper, we have introduced a new class of preinvexity namely hyperbolic type harmonic preinvex functions and to support this new defi- nition, some of its algebraic properties are elaborated. By using this new class of preinvexity, we have established a few Hermite-Hadamard type integral inequalities. Some novel refinements of Hemite-Hadamard type inequalities for hyperbolic type harmonic preinvex functions are presented as well. Finally, the Riemann-Liouville fractional version of the Hermite-Hadamard Inequality is established. [ABSTRACT FROM AUTHOR]

In this paper, only under the q - k -Keller–Osserman conditions, we consider the existence and global estimates of innumerable radial q - k -convex positive solutions to the q - k -Hessian equation and systems. Our conditions are strictly weaker than those in previous papers. [ABSTRACT FROM AUTHOR]

In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping f || 1/6 [f(A) x 1 + 4f - A - 1 + 1 B 2 - + 1 f(B) - - Z 1 0 f((1 - k)A < 1 + k1 B)dk || 5\36 1 B-A 1 f'I,+8. [ABSTRACT FROM AUTHOR]

In this paper we show that inequalities for functions convex on the coordinates can be derived from inequalities for convex functions defined on real intervals, and essentially only this method works. As applications, we show how our result works for the Jensen's and Hermite- Hadamard inequalities for functions convex on the coordinates. Finally, we extend the classical notion of f -divergence functional to functions convex on the coordinates, and as a further application of our main result, we study the refinement of a basic inequality corresponding to the new divergence. [ABSTRACT FROM AUTHOR]

This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order β approaches 1, in addition to the fractional integrals we examined. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of bilevel programming problems (BLPP) in the framework of Euclidean space. We derive relationships among the solutions of approximate Minty-type variational inequalities (AMTVI), approximate Stampacchia-type variational inequalities (ASTVI), and local ϵ -quasi solutions of the BLPP, under generalized approximate convexity assumptions, via limiting subdifferentials. Moreover, by employing the generalized Knaster–Kuratowski–Mazurkiewicz (KKM)-Fan's lemma, we derive some existence results for the solutions of AMTVI and ASTVI. We have furnished suitable, non-trivial, illustrative examples to demonstrate the importance of the established results. To the best of our knowledge, there is no research paper available in the literature that explores relationships between the approximate variational inequalities and BLPP under the assumptions of generalized approximate convexity by employing the powerful tool of limiting subdifferentials. [ABSTRACT FROM AUTHOR]

In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q -symmetric starlike and q -symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q -analogue Salagean integral operator, the p -valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p -valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ , q -neighborhoods for p -valent functions are defined. In relation to symmetric δ , q -neighborhoods of q -symmetric p -valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q -symmetric inequalities of analytic functions with negative coefficients is also provided. [ABSTRACT FROM AUTHOR]

In continuation of Zayed and Bulboacă work in (J. Inequal. Appl. 2022:158, 2022), this paper discusses the geometric characterization of the normalized form of the generalized Bessel function defined by V ρ , r (z) : = z + ∑ k = 1 ∞ (− r) k 4 k (1) k (ρ) k z k + 1 , z ∈ U , for ρ , r ∈ C ∗ : = C ∖ { 0 } . Precisely, we will use a sharp estimate for the Pochhammer symbol, that is, Γ (a + n) / Γ (a + 1) > (a + α) n − 1 , or equivalently (a) n > a (a + α) n − 1 , that was firstly proved by Baricz and Ponnusamy for n ∈ N ∖ { 1 , 2 } , a > 0 and α ∈ [ 0 , 1.302775637 ... ] in (Integral Transforms Spec. Funct. 21(9):641–653, 2010), and then proved in our paper by another method to improve it using the partial derivatives and the two-variable functions' extremum technique for n ∈ N ∖ { 1 , 2 } , a > 0 and 0 ≤ α ≤ 2 , and used to investigate the orders of starlikeness and convexity. We provide the reader with some examples to illustrate the efficiency of our theory. Our results improve, complement, and generalize some well-known (nonsharp) estimates, as seen in the Concluding Remarks and Outlook section. [ABSTRACT FROM AUTHOR]

It is well known that the recursive least squares (RLS) algorithm is renowned for its rapid convergence and excellent tracking capability. However, its performance is significantly compromised when the system is sparse or when the input signals are contaminated by impulse noise. Therefore, in this paper, the minimum error entropy (MEE) criterion is introduced into the cost function of the RLS algorithm in this paper, with the aim of counteracting the interference from impulse noise. To address the sparse characteristics of the system, we employ a universally applicable convex function to regularize the cost function. The resulting new algorithm is named the convex regularization recursive minimum error entropy (CR-RMEE) algorithm. Simulation results indicate that the performance of the CR-RMEE algorithm surpasses that of other similar algorithms, and the new algorithm excels not only in scenarios with sparse systems but also demonstrates strong robustness against pulse noise. [ABSTRACT FROM AUTHOR]

For the adjacency matrix A(G) and diagonal matrix of the vertex degrees D(G) of a simple graph G, the A(G) matrix is the convex combinations of D(G) and A(G), and is defined as A(G) = D(G)+(1)A(G), for 0 n be the eigenvalues of A(G) (which we call -adjacency eigenvalues of the graph G). The generalized adjacency energy also called -adjacency energy of the graph G is defined as EA (G) = is the average vertex degree, m is the size and n is the order of G. The -adjacency energy of a graph G merges the theory of energy (adjacency energy) and the signless Laplacian energy, as EA0 (G) = E (G) and 2E A 12 (G) = QE(G), where E (G) is the energy and QE(G) is the signless Laplacian energy of G. In this paper, we obtain some new upper and lower bounds for the generalized adjacency energy of a graph, in terms of different graph parameters like the vertex covering number, the Zagreb index, the number of edges, the number of vertices, etc. We characterize the extremal graphs attained these bounds. [ABSTRACT FROM AUTHOR]

DC (difference of convex functions) programming and DC algorithm (DCA) are powerful tools for nonsmooth nonconvex optimization. This field was created in 1985 by Pham Dinh Tao in its preliminary state, then the intensive research of the authors of this paper has led to decisive developments since 1993, and has now become classic and increasingly popular worldwide. For 35 years from their birthday, these theoretical and algorithmic tools have been greatly enriched, thanks to a lot of their applications, by researchers and practitioners in the world, to model and solve nonconvex programs from many fields of applied sciences. This paper is devoted to key open issues, recent advances and trends in the development of these tools to meet the growing need for nonconvex programming and global optimization. We first give an outline in foundations of DC programming and DCA which permits us to highlight the philosophy of these tools, discuss key issues, formulate open problems, and bring relevant answers. After outlining key open issues that require deeper and more appropriate investigations, we will present recent advances and ongoing works in these issues. They turn around novel solution techniques in order to improve DCA's efficiency and scalability, a new generation of algorithms beyond the standard framework of DC programming and DCA for large-dimensional DC programs and DC learning with Big data, as well as for broader classes of nonconvex problems beyond DC programs. [ABSTRACT FROM AUTHOR]

Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [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]

This paper is intended to provide an updated survey of recent optimality theory for infinite-dimensional convex programming. It aims at establishing theoretical support for algorithmic developments. Two alternative strategies inspire the approaches presented in the paper. The first one consists of replacing the family of constraints by a single one, appealing to the supremum function, and is based on various characterizations of the subdifferential of the pointwise supremum of convex functions. The second one uses appropriate characterizations of affine consequent inequalities of the constraint system exploiting ad hoc constraint qualifications. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new inequalities of Hermite–Hadamard type for differentiable functions with h-convex derivatives. It is also shown that the newly established inequalities are extension of the existing inequalities in the literature. Finally, we give applications of the new results and outline some future problems. [ABSTRACT FROM AUTHOR]

Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the form of new estimates for so-called strong f-divergences: the concept of the Csiszár f-divergence for strongly convex functions f, together with particular cases (Kullback–Leibler divergence, χ 2 -divergence, Hellinger divergence, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence.) Furthermore, new estimates for the Shannon entropy are obtained, and new Chebyshev-type inequalities are derived. [ABSTRACT FROM AUTHOR]

Differential subordination in the complex plane is the generalization of a differential inequality on the real line. In this paper, we consider two subclasses of univalent functions associated with the trigonometric function cos z. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter β such that the analytic function p(z) satisfying p(0) = 1, is subordinate to cos z when the differential expression p(z) + βz(dp(z)/dz) is subordinate to the Janowski function. We compute sharp bounds on coefficient functional Hermitian-Toeplitz determinants of the third and the fourth order with an invariance property for such functions. In addition, we estimate bound on Hankel determinants of the second and the third order. [ABSTRACT FROM AUTHOR]

To obtain the main result of the present paper, we use the technique of differential superordination. As special cases of our main result, we obtain sufficient conditions for f 2 A to be Φ-like, parabolic Φ-like, starlike, parabolic starlike, close-to-convex and uniform close-to-convex. We also obtain sandwich-type results regarding these functions. For demonstration of the results, we have plotted the images of open unit disk under certain functions using Mathematica 7.0. [ABSTRACT FROM AUTHOR]

This paper focuses on introducing and investigating the class of generalized n-fractional polynomial s-type convex functions within the framework of fractional calculus. Relationships between the novel class of functions and other kinds of convex functions are given. New integral inequalities of Hermite-Hadamard and Ostrowski-type are established for our novel generalized class of convex functions. Using some identities and fractional operators, new refinements of Ostrowskitype inequalities are presented for generalized n-fractional polynomial s-type convex functions. Some special cases of the newly obtained results are discussed. It has been presented that, under some certain conditions, the class of generalized n-fractional polynomial s-type convex functions reduces to a novel class of convex functions. It is interesting that, our results for particular cases recaptures the RiemannLiouville fractional integral inequalities and quadrature rules. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes, and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive algorithm with multi-step inertia for solving a convex bilevel optimization problem. Under suitable parameter conditions, we prove that our algorithm converges strongly to some solution of the problem, which is the unique solution to some variational inequality problem. The effectiveness of the proposed algorithm is verified by numerical experiments and compared with other algorithms. [ABSTRACT FROM AUTHOR]

Two typical fixed-length random number generation problems in information theory are considered for general sources. One is the source resolvability problem and the other is the intrinsic randomness problem. In each of these problems, the optimum achievable rate with respect to the given approximation measure is one of our main concerns and has been characterized using two different information quantities: the information spectrum and the smooth Rényi entropy. Recently, optimum achievable rates with respect to f-divergences have been characterized using the information spectrum quantity. The f-divergence is a general non-negative measure between two probability distributions on the basis of a convex function f. The class of f-divergences includes several important measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence, it is meaningful to consider the random number generation problems with respect to f-divergences. However, optimum achievable rates with respect to f-divergences using the smooth Rényi entropy have not been clarified yet in both problems. In this paper, we try to analyze the optimum achievable rates using the smooth Rényi entropy and to extend the class of f-divergence. To do so, we first derive general formulas of the first-order optimum achievable rates with respect to f-divergences in both problems under the same conditions as imposed by previous studies. Next, we relax the conditions on f-divergence and generalize the obtained general formulas. Then, we particularize our general formulas to several specified functions f. As a result, we reveal that it is easy to derive optimum achievable rates for several important measures from our general formulas. Furthermore, a kind of duality between the resolvability and the intrinsic randomness is revealed in terms of the smooth Rényi entropy. Second-order optimum achievable rates and optimistic achievable rates are also investigated. [ABSTRACT FROM AUTHOR]

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences. [ABSTRACT FROM AUTHOR]

In this research, we demonstrate novel Hermite–Hadamard–Mercer fractional integral inequalities using a wide class of fractional integral operators (the Raina fractional operator). Moreover, a new lemma of this type is proved, and new identities are obtained using the definition of convex function. In addition to a detailed derivation of a few special situations, certain known findings are summarized. We also point out that some results in this study, in some special cases, such as setting α = 0 = φ , γ = 1 , and w = 0 , σ (0) = 1 , λ = 1 , are more reasonable than those obtained. Finally, it is believed that the technique presented in this paper will encourage additional study in this field. [ABSTRACT FROM AUTHOR]

In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a 2 and a 3 for functions in these subclasses. Using the values of a 2 and a 3 , we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof. [ABSTRACT FROM AUTHOR]

To solve a distributed optimal resource allocation problem, a collective neurodynamic approach based on recurrent neural networks (RNNs) is proposed in this paper. Multiple RNNs cooperatively solve a global constrained optimization problem in which the objective function is a total of local non-smooth convex functions and is subject to local convex sets and a global equality constraint. Different from the projection dynamics to deal with local convex sets in the existing work, an internal dynamics with projection output is designed in the algorithm to relax the Slater's condition satisfied by the optimal solution. To overcome continuous-time communication in a group of RNNs, an aperiodic communication scheme, called the event-triggered scheme, is presented to alleviate communication burden. It is analyzed that the convergence of the designed collective neurodynamic approach based on the event-triggered communication does not rely on global information. Furthermore, it is proved the freeness of the Zeno behavior in the event-triggered scheme. Two examples are presented to illustrate the obtained results [ABSTRACT FROM AUTHOR]

In multi-objective mixed-integer convex optimization, multiple convex objective functions need to be optimized simultaneously while some of the variables are restricted to take integer values. In this paper, we present a new algorithm to compute an enclosure of the nondominated set of such optimization problems. More precisely, we decompose the multi-objective mixed-integer convex optimization problem into several multi-objective continuous convex optimization problems, which we refer to as patches. We then dynamically compute and improve coverages of the nondominated sets of those patches to finally combine them to obtain an enclosure of the nondominated set of the multi-objective mixed-integer convex optimization problem. Additionally, we introduce a mechanism to reduce the number of patches that need to be considered in total. Our new algorithm is the first of its kind and guaranteed to return an enclosure of prescribed quality within a finite number of iterations. For selected numerical test instances we compare our new criterion space based approach to other algorithms from the literature and show that much larger instances can be solved with our new algorithm. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a subclass of starlike functions introduced by Silverman. It is defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the sharp bounds of coefficient problems for the inverse of functions in this class. We derive the upper bounds of some initial coefficients, the Fekete–Szegö type inequality and the second Hankel determinant for . On the third Hankel determinant , we give a bound on the inverse of . All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the optimality conditions for a class of nonsmooth multiobjective fractional optimization problems subject to vanishing constraints. In particular, necessary and sufficient conditions for (weak) Pareto solution are presented in terms of the Clark subdifferential. Furthermore, we construct Wolfe and Mond–Weir-type dual models and derive some duality theorems by using generalized quasiconvexity assumptions. Some examples to show the validity of our conclusions are provided. [ABSTRACT FROM AUTHOR]

In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for χ -divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski's inequality, trapezoidal inequality, midpoint inequality, Simpson's inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of γ and parameter ξ. [ABSTRACT FROM AUTHOR]

In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference Φ(f (A)) -- f (Φ (A)) for any convex function f : I → R, any selfadjoint operator A in H with the spectrum Sp (A) ⊂ I and any linear, positive and normalized map Φ : B (H) → B (K), where H and K are Hilbert spaces. Some examples of convex and operator convex functions are also provided. [ABSTRACT FROM AUTHOR]

In this paper, we estimate sharp bounds for certain Hankel determinants, H2,3(f), H3,1(f) and Zalcman functional |a²3 -- a5| for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135. [ABSTRACT FROM AUTHOR]

In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities of the form.. are obtained with variations due to the convexity properties of the mapping f. [ABSTRACT FROM AUTHOR]

In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint operators in Hilbert spaces have several tensorial norm inequalities discovered in this study. The convexity features of the mapping f lead to the variation in several inequalities of the trapezoid type. [ABSTRACT FROM AUTHOR]

This paper aims to find generalizations of inequalities that hold for unified integral operators by applying strongly exponentially (α, ℏ − m) − p‐convex functions. These inequalities generate results for several fractional integral operators and simultaneously hold for convex, strongly convex, and exponentially convex functions. The particular cases of presented inequalities are directly connected with many recently published results. [ABSTRACT FROM AUTHOR]

This paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations. [ABSTRACT FROM AUTHOR]

We extend the parametric method developed for the van der Waals model by Lekner [Am. J. Phys. 50(2), 161–163 (1982)] to other equations of state, particularly the Berthelot model, thereby making the testing of these equations of state much faster and simpler. We systematically investigate important properties of first-order phase transitions in the Berthelot model. Thermodynamic properties near the critical point are discussed and the predictions of the Berthelot and van der Waals models are compared with experimental data. The Berthelot equation affords an improved fit to the density–temperature coexistence curve for many substances when compared to the van der Waals equation. A failure of the Berthelot model is its prediction of latent heat and heat capacities that are convex functions at lower temperatures. We also examine two modifications of the Berthelot equation of state that, like the van der Waals model, are also solvable by the parameter method. These, which we call the cPF and dPF models, reduce to the van der Waals and Berthelot models in different limits of their parameters. They give improved fits to the experimental data away from the critical point but involve an additional fitting parameter. Editor's note: While the van der Waals equation of state provides a simple model for phase transitions, it fails to achieve a good quantitative fit for properties near phase transitions in most substances. A closely related model, the Berthelot model, still has only two free parameters, but it allows the attraction between molecules to depend not only on volume but also on temperature. This paper builds on the parametric expressions for the van der Waals gas derived in a 1982 paper in this journal by John Lekner. It shows that similar expressions derived from the Berthelot model provide a much better fit to the data. This derivation could be shared with students in intermediate or advanced thermodynamics courses. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a linear operator and define a certain class Ep(a, c, λ, γ: h) of analytic and multivalent functions in the open unit disk associated with differential subordination. Also, we discuss some geometric properties for this class. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study certain geometric properties of a class of analytic functions involving the Barnes–Mittag-Leffler function. The main mathematical tools are the monotonicity patterns of some class of functions associated with the gamma and digamma functions. Furthermore, some consequences and examples are presented. [ABSTRACT FROM AUTHOR]

This paper aims to examine an approach that studies many Euler–Maclaurin-type inequalities for various function classes applying Riemann–Liouville fractional integrals. Afterwards, our results are provided by using special cases of obtained theorems and examples. Moreover, several Euler–Maclaurin-type inequalities are presented for bounded functions by fractional integrals. Some fractional Euler–Maclaurin-type inequalities are established for Lipschitzian functions. Finally, several Euler–Maclaurin-type inequalities are constructed by fractional integrals of bounded variation. [ABSTRACT FROM AUTHOR]

In this paper, we shall find the order of starlikeness and convexity for integral operators Fαj,βj,λj,ζ (z) = {ζ ∫0z tζ−1 πnj=1 (Eαj,βj(t)/t )1/λj dt}1/ζ, where the functions Eαj,βj are the normalized Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed approximate subgradient-type method for minimizing a sum of differentiable and non-differentiable convex functions subject to nondifferentiable convex functional constraints in a Euclidean space. We establish the convergence of the sequence generated by our method to an optimal solution of the problem under consideration. Moreover, we derive a convergence rate of order O(N1−a) for the objective function values, where a ∈ (0.5, 1). Finally, we provide a numerical example illustrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by García-Castaño, Melguizo-Padial and Parzanese (2023, Math. Meth. Oper. Res. 97). [ABSTRACT FROM AUTHOR]

In this paper, we consider an inexact projected gradient method equipped with a nonmonotone line search rule for smooth constrained multiobjective optimization. In this method, a new nonmonotone line search technique proposed here is employed and the relative errors on the search direction is admitted. We demonstrate that this method is well-defined. Then, we prove that each accumulation point of the sequence generated by this method is Pareto stationary and analyze the convergence rate of the algorithm. When the objective function is convex, the convergence of the sequence to a weak Pareto optimal point of the problem is established. [ABSTRACT FROM AUTHOR]

In this paper, we have analysed the influence of viscoelastic and frictional damping on the decay rate of solutions for a Kirchhoff-type viscoelastic wave equation with a distributed delay acting on nonlinear internal damping. Taking the relaxation function of a fairly large class and using the method of energy in which we introduce an adapted Lyapunov functional and by exploiting certain properties of convex functions, under certain assumptions on the constants of system, we obtain the optimal decay rate of energy in the sense that it is compatible with the decay rate of the relaxation function. [ABSTRACT FROM AUTHOR]