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We extend the inventory lot-size model in this paper to allow for products to deteriorate at variable rates, and demand is characterized by any log concave function of time that fulfils relatively mild criteria. Partial backlogging is possible with this model. The backlogging rate is a time-dependent, exponentially declining function provided by a parameter. We show that not only does the optimal replacement schedule exist, but that it is also unique. We also show that the inventory system's overall cost is a convex function of the number of replenishments. As a result, identifying a local minimum simplifies the search for the best number of replenishments. Finally, a numerical example is given to demonstrate the findings. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to introduce and investigate a novel subclass of analytic functions in the open unit disk by generalizing the Srivastava-Attiya operator. So by using the generalization we have introduced a subclass of analytic function with negative coefficients in the unit disk. We have referred to the previous studies that used the Sirvastava-Attiya operator and generalized it, explained the functions of the class 퓐 and the basic definitions that included this paper. We used some important lemmas from previous studies to prove our results, and we obtained some important geometric properties of the analytical functions. We proved the theorem of growth and destortion, and we showed the cofficient bound, extreme points of the functions in this class, in addition to the radii of the starlike, convex and close-to-convex functions of order 휑. Finally, we defined the 훼 −neighborhood and showed the relationship between the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ (γ , ρ , l , σ) and the functions that belong to the class S ⌣ λ p , μ q , t s , a , λ , ω (γ , ρ , l , σ). [ABSTRACT FROM AUTHOR]

The paper is focused on solution of the kinematic limit analysis problem arising in geotechnical stability assessment. This problem may be classified as conic optimization and for its solution, the Augmented Lagrangian method with adaptive penalty is proposed to enforce equality constraints. The corresponding inner problem leads to the minimization of a convex quadratic function on a closed convex feasible set defined by separable cones and it is solved by projected gradients with spectral step-lengths. The efficiency of the suggested solver is demonstrated on a strip-footing benchmark problem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same. [ABSTRACT FROM AUTHOR]

The effectiveness of stochastic gradient methods strongly depends on a suitable selection of the hyperparameters which define them. Particularly, in the context of large-scale optimization problems often arising in machine learning applications, to properly fix both the learning rate and the mini-batch size in the definition of the stochastic directions is crucial for obtaining fast and efficient learning procedures. In a recent paper [1], the authors propose to define these hyperparameters by combining an adaptive subsampling strategy and a line search scheme. The aim of this work is to adapt this idea to both the stochastic gradient algorithm with momentum and the AdaM method in order to exploit the good numerical behaviour of the momentum-like stochastic gradient methods and the automatic technique to select the hyperparameters discussed in [1]. An extensive numerical experimentation carried out on convex functions, with different data sets, highlights that such combined hyperparameters technique makes the tuning of the hyperparameters computationally less expensive than the selection of suitable constant learning rate and mini-batch size and this is significant from the perspective of GreenAI. Furthermore, the proposed versions of the stochastic gradient method with momentum and AdaM have promising convergence behaviour compared to the original counterparts. [ABSTRACT FROM AUTHOR]

The paper presents one important and interesting property of strictly convex functions. On the base of previously proved properties of these functions, we can generalize some global-geometric conclusions, without the even assumption of their differentiability, and also point out some geometric characteristics of the sets of all solutions of parametric optimization problems. Two specific nonlinear parametric optimizations of nonlinear problems -- the minimization and the maximization problems -- exist for them. They express a pair of dual optimization problems. The set of all optimal points has an important geometric interpretation. This paper connects the proved properties of a specific case and a geometric sense. [ABSTRACT FROM AUTHOR]

In the present paper, we consider and investigate a certain class of close-to-convex functions that defined in the unit disk, U = {z : |z| <1}, which denotes as Re{eiα zf'(z)/f(z)-f(-z)} > δ where |α| < π, cos (α) > δ and 0 ≤ δ < 1. Furthermore, we obtain preliminary result for bound f'(z) and determine result for radius of convexity. [ABSTRACT FROM AUTHOR]

In this paper, we present convex hull formulations for a mixed-integer, multilinear term/function (MIMF) that features products of multiple continuous and binary variables. We develop two equivalent convex relaxations of an MIMF and study their polyhedral properties in their corresponding higher-dimensional spaces. We numerically observe that the proposed formulations consistently perform better than state-of-the-art relaxation approaches. [ABSTRACT FROM AUTHOR]

In this paper, we established some new integral inequalities of Hadamard-type for co-ordinated convex functions by using a new integral identity and fairly elementary analysis. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new integral inequalities for co-ordinated m --convex functions by using a new integral identity and basic definitions. We also give some reduced results by selecting special value of parameter m. [ABSTRACT FROM AUTHOR]

In this paper, firstly a new integral equality is proved and based on this equality some new integral inequalities of Hadamard type are given for differentiable Geometric convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m- convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

This paper examines the estimation of the best weighted approximation and (co)convex functions with varying degrees of polynomial order. There are some situations in which the estimation of the best approximation is not well equipped to deal with the (co)convex and unconstrained polynomial (COCUNP) approximation and the reduction of the control of the rate errors of approximation. The weighted Ditzian-Totik moduli of smoothness (DTMS) and Lebesgue Stieltjes integral are employed to prove. The developed estimate is able to priority unconstrained approximation. [ABSTRACT FROM AUTHOR]

The Hermite-Hadamard type inequality has been extended to some classes of convex functions and composite convex functions. In this paper, we refine the definition of composite-ɸ−1 convex function and definition of m-convex function to define the composite-ɸ−1m-convex functions. From the definition, we obtain some inequalities related to GA-m-convexity, HA-m-convexity, p-m-convexity and LogExp m-convexity. Next, k-composite-ɸ−1m-convex function is defined. Some inequalities of Hermite-Hadamard type for composite-ɸ−1m-convex functions and k-composite-ɸ−1m-convex functions are obtained. From the inequalities obtained, we provide some applications for GG, AG, HA and HH convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we established new inequalities of Hermite-Hadamard-Fejér type for Riemann-Liouville and conformable fractional integrals. [ABSTRACT FROM AUTHOR]

In this paper, we define (h, m) --convex functions on Δ = [a, b] x [x, d] and obtain some properties of this new class of functions. We also prove a new generalization of Hadamard inequality on the co-ordinates. [ABSTRACT FROM AUTHOR]

In this paper, we consider the class Kα* of the functions of the form f(z) = z+a2z2+... which are analytic univalent in the disc D = {z:|z|<1} such that Reα(z2f"(z))′/g′(z)+(zf′(z))′/g;(z)>0 where g ∈ C. This paper focuses on the functional |a2a4-a32| for a function belonging to Kα* is obtained. [ABSTRACT FROM AUTHOR]

In the paper one focuses on a mathematical problem, which is to be formulated in case of treatment of a class of structural problems, in order to properly represent the behavior of the structure, like, for example, in case of mechanical non-linearity of the material. The analytical formulation is presented allowing to identify a set of functions enjoying some special properties, whose combination allows to achieve the problem solution. [ABSTRACT FROM AUTHOR]

The object of this paper is to obtain the estimate for second Hankel determinant | a 2 a 2 − a 3 2 | of Ma-Minda starlike and convex functions. Also obtain the estimates for | h 1 h 3 − h 2 2 | of the functions associated with z f (z) . [ABSTRACT FROM AUTHOR]

In this paper the functions F(z) which are q–valent starlike and convex function of order γ, also ϑ–spirallike of order γ within the open unit disk Λ, a few interesting enough conditions concerning coefficient inequalities for positive subcategory of regular and q–valent functions for F(z) are discussed. Many special instances and consequences of those coefficient inequalities are also considered. [ABSTRACT FROM AUTHOR]

In this paper we establish some new integral inequalities analogous to the Opial inequality by using the proved lemma and some classical inequalities for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we establish Hermite-Hadamard type inequalities for Riemann- Liouville integrals via (α, m)-geometrically convex funtions. [ABSTRACT FROM AUTHOR]

In this paper, new integral inequalities of Hermite-Hadamard type are developed for n-times differentiable quasi-convex functions. [ABSTRACT FROM AUTHOR]

In this paper, some new Hermite-Hadamard type inequalities involving fractional integrals for s-convex functions in the second sense are derived. [ABSTRACT FROM AUTHOR]

in this paper, we gave the new general identity for differentiable function. As a result of this identity some new and general fractional integral inequalities for differentiable GA-convex functions are obtained. [ABSTRACT FROM AUTHOR]

The paper addresses the nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions. The original problem is reduced to a problem without constraints with the help of the exact penalization theory. After that, the penalized problem is represented as a d.c. minimization problem without constraints, for which the new mathematical tools under the form of global optimality conditions (GOCs) are developed. The GOCs reduce the nonconvex problem in question to a family of convex (linearized with respect to the basic nonconvexities) problems. On the base of the proposed theory we develop numerical methods of local and global search for the problem in question. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded. [ABSTRACT FROM AUTHOR]

In this paper, it is defined the operator GA-convex functions for continuous functions of self-adjoint operators in Hilbert spaces. And then it is obtained some new Hermite-Hadamard type inequalities for this class of functions. [ABSTRACT FROM AUTHOR]

In this study, by using convex functions, we first establish new refinements of Hermite-Hadamard-Fejer type inequalities via Riemann-Liouville fractional integral operators. The results given in this paper provide generalization of several inequalities obtained in earlier studies. [ABSTRACT FROM AUTHOR]

In this paper we proved some new Hadamard-type inequalities for h-convex functions. [ABSTRACT FROM AUTHOR]

Isermann (1978) established that every efficient solution of optimization problem is properly efficient if the objective functions are linear and feasible set is polyhedral. Choo (1984) proved this result when the objective functions are linear fractional and the feasible set is a compact polyhedron. Chew and Choo (1984) established that every efficient solution of optimization problem which satisfies the following boundedness condition is properly efficient if all the objective functions and constraint functions are pseudolinear. A feasible point χ∈Χ is said to satisfy the boundedness condition if the set {Pi(χ*,χ)Pj(χ*,χ):fi(χ)i(χ*),fj(χ)>fj(χ*),1≤i,j≤κ} is bounded above, where pi is a proportional function corresponding to fi,i = 1,2,3,.........κ. Gulati and Islam (1990) have shown that the above result still holds if we take the objective functions to be pseudolinear, constraint functions to be quasiconvex and certain constraint qualification is satisfied. In this paper we show that every efficient solution that satisfies the above boundedness condition and generalized constraint qualification, is properly efficient if all the objective functions and constraint functions defined on a convex set are semilocally pseudolinear and their right differentials at that efficient solution are convex. [ABSTRACT FROM AUTHOR]

This paper considers investigating properties of a new subclasses of strongly starlike functions defined using a new proposed operator. These properties include inclusion properties. [ABSTRACT FROM AUTHOR]

In this paper, using the identity obtained by Yaldız and Sarıkaya in [10], some new Hermite-Hadamard type inequalities for quasi-convex functions via fractional integral operators are given. [ABSTRACT FROM AUTHOR]

Bullen-type and Simpson-type inequalities involving convex functions have established in [7]. In this paper, some new results have been obtained for a large class of convex functions: quasi-convex. Applications for Beta function are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we give a new integral identity for differentiable functions and by using this identity we establish some new type integral inequalities for the class of functions whose derivatives in absolutely value at certain powers are p-convex. Also, we give some applications to special means of positive real numbers [ABSTRACT FROM AUTHOR]

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, and thus establish a new calculus, called Non-Newtonian Calculus. So, in this paper, it is investigated to the convex functions and some inequalities in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus. [ABSTRACT FROM AUTHOR]

In the present paper, several interesting integral inequalities involving fractional integral operators for different class of convex mappings are established. Our results in a special case yield results obtained by via Riemann-Liouville fractional integrals. Therefore, the results presented here would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, using integral representations for n--times differentiable mappings, we establish new generalizations of certain Hermite-Hadamard type inequality for quasiconvex functions. We also give some new estimations for special means of real numbers. [ABSTRACT FROM AUTHOR]

In 2011, Lennard and Nezir showed that very large class of closed bounded convex sets in c0 fails the fixed point property for affine nonexpansive mappings respect to c0's usual norm since they proved that closed convex hull of any asymptotically isometric (ai) c0-summing basis fails the fixed point property for nonexpansive mappings and in fact their class is one of these. Then, Nezir recently worked on these sets and constructed several equivalent norms. In one of his works, he defined the equivalent norm ΙΙΙ·ΙΙΙ on c0 by ... for all x ∈ c0. Then, he studied a subclass of the class S below introduced by Lennard and Nezir and showed that it has the fixed point property for affine ΙΙΙ·ΙΙΙ-nonexpansive mappings for some α > 1 when Q1 > 1-γ1+ΙαΙ/1+2ΙαΙ ... In this paper, we will show that the below larger class G given by Lennard and Nezir that contains S has the fixed point property for affine ΙΙΙ·ΙΙΙ-nonexpansive mappings for all α > 1 when Q1 > 1-γ1+ΙαΙ/1+2ΙαΙ ... Moreover and most importantly, we generalize our results for the closed convex hull of the sequence ηη = γη (b1e1 + b2e2 + ... + bnen) when 0 < bn and 0 γn are arbitrarily choosen. [ABSTRACT FROM AUTHOR]

Suppose Λ is a finitely aligned k-graph. In this paper we present some conditions for the k-graph Λ in order the complex Kumjian-Pask algebra KPC(Λ)is finite dimensional. This is an improvement for the previous results when the k-graph Λ is row finite without sources and when Λ is locally convex row finite kgraph. We also characterise simple Kumjian-Pask algebra KPR(Λ). [ABSTRACT FROM AUTHOR]

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product or convolution. A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also consider several applications of our main results to the generalized hypergeometric functions. [ABSTRACT FROM AUTHOR]

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived. [ABSTRACT FROM AUTHOR]

Shepard's method is a well-known technique for interpolating large sets of scattered data. The classical Shepard operator reconstructs an unknown function as a normalized blend of the function values at the scattered points, using the inverse distances to the scattered points as weight functions. Based on the general idea of defining interpolants by convex combinations, Little suggested to extend the bivariate Shepard operator in two ways. On the one hand, he considers a triangulation of the scattered points and substitutes function values with linear polynomials which locally interpolate the given data at the vertices of each triangle. On the other hand, he modifies the classical point-based weight functions and defines instead a normalized blend of the locally interpolating polynomials with triangle-based weight functions which depend on the product of inverse distances to the three vertices of the corresponding triangle. The resulting triangular Shepard operator interpolates all data required for its definition and reproduces polynomials up to degree 1, whereas the classical Shepard operator reproduces only constants, and has quadratic approximation order. In this paper we discuss an improvement of the triangular Shepard operator. [ABSTRACT FROM AUTHOR]

Many generalizations of convex functions have been appeared in the literature. We consider some classes of generalized convex functions namely B-vex function, B-preinvex function and (α λ)-convex function. These functions play a significant role in optimization theory and applied science. The purpose of this paper is to study these generalizations under differentiability. [ABSTRACT FROM AUTHOR]

In this paper, a version of Hermite Hadamard-type inequalities for (d,t)-convex functions are established. And then we give some new inequalities of the Hermite-Hadamard type for the product of two (d, t)-convex functions. [ABSTRACT FROM AUTHOR]

The main aim of the present paper is to introduce φh-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φh-convex stochastic processes. We also give some new general inequalities for φh-convex stochastic processes. [ABSTRACT FROM AUTHOR]

In this paper, we prove some new inequalities for the functions whose derivatives in absolute values are m-convex. We obtain generalized inequalities which have the property of giving Hadamard, Ostrowski and Simpson type results by changing parameter. [ABSTRACT FROM AUTHOR]

In this paper, the Authors establish some new Hermite-Hadamard type inequalities for (β, α; n, m) -logarithmic and (β, α; n, m)-Godunova-Levin-log-convex functions. Some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, some new integral inequalities will be given using generalized Hermite-Hadamard's type integral inequalities holding for m-convex functions. Our results presented here would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In this present paper, some new generalized Hermite-Hadamard type inequalities for functions whose second derivatives in absolute value are generalized s-convex in the second sense are obtained. [ABSTRACT FROM AUTHOR]