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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]

If a subset of vertices of a graph, designed in such a way that the remaining vertices have unique identification (usually called representations) with respect to the selected subset, then this subset is named as a metric basis (or resolving set). The minimum count of the elements of this subset is called as metric dimension. This concept opens the gate for different new parameters, like faulttolerant metric dimension, in which the failure of any member of the designed subset is tolerated and the remaining subset fulfills the requirements of the resolving set. In the pattern of the resolving sets, a concept was introduced where the representations of edges must be unique instead of vertices. This concept was called the edge metric dimension, and this as well as the previously mentioned concepts belong to the idea of resolvability parameters in graph theory. In this paper, we find all the above resolving parametric sets of a convex polytope F♃ and compare their cardinalities. [ABSTRACT FROM AUTHOR]

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p = 2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles. [ABSTRACT FROM AUTHOR]

In this paper we prove some properties for functions that are multivalent in the unit disc |z| < 1 in the complex plane. As a corollary we obtain that if f(z) is p-valent, p ≥ 10, and |arg{f(p)(z)}|<π in |z| < 1, then f (z) is p-valent starlike. [ABSTRACT FROM AUTHOR]

The theory of geometric functions was first introduced by Bernard Riemann in 1851. In 1916, with the concept of normalized function revealed by Bieberbach, univalent function concept has found application area. Assume f(z)=z+Σn>2(anzn converges for all complex numbers z with 1,|z|, and f(z)is one-to-one on the set of such z. Convex and starlike functions f(z) and g(z) are discussed with the help of subordination. The f(z) and g(z) are analytic in unit disc and f(0)0,f'(0)=1, and g(0)=0,g'(0)-1=0. A single valued function f(z) is said to be univalent (or schlict or one-to-one) in domain DCC never gets the same value twice; that is, if f(x1)-fz2 for all z1 and z2 with z1= z2. Let A be the class of analytic functions in the unit disk U={z:|z|1} that are normalized with f(0)=0,f'(0)=1. In this paper we give the some necessary conditions for f(z)E S*[a,a²] and 0< a²-r. [ABSTRACT FROM AUTHOR]

In this paper, the CQN_Chen function is used to characterize the plastic anisotropic evolution of 304 stainless steel (SS304). The uniaxial tensile tests along different loading directions are conducted to experimentally investigate the anisotropic hardening behavior for SS304. The experimental data indicates that the anisotropy of SS304 is weak. The convexity analysis is carried out by the geometry-inspired numerical convex analysis method for the CQN_Chen yield locus during plastic deformation. The Hill48, SY2009 and CQN functions are used as the comparison to evaluate the accuracy of the CQN_Chen function in characterizing plastic evolution. The predicted values are compared with the experimental data. The comparison demonstrates that the CQN_Chen function can accurately characterize anisotropic hardening behavior under uniaxial tension along distinct loading directions and equibiaxial tension. Simultaneously, the CQN_Chen model has the capacity to adjust the yield surface shape between uniaxial tension and equibiaxial tension. The CQN_Chen model is recommended to characterize plastic evolving behavior under uniaxial tension along different directions and equibiaxial tension. [ABSTRACT FROM AUTHOR]

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the 1q and 2q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations. [ABSTRACT FROM AUTHOR]

The normalization of the combination of generalized Lommel–Wright function J κ 1 , κ 2 κ 3 , m (z) (m ∈ N , κ 3 > 0 and κ 1 , κ 2 ∈ C ) defined by J κ 1 , κ 2 κ 3 , m (z) : = Γ m (κ 1 + 1) Γ (κ 1 + κ 2 + 1) 2 2 κ 1 + κ 2 z 1 − (κ 2 / 2) − κ 1 J κ 1 , κ 2 κ 3 , m (z) , where J κ 1 , κ 2 κ 3 , m (z) : = (1 − 2 κ 1 − κ 2) J κ 1 , κ 2 κ 3 , m (z) + z (J κ 1 , κ 2 κ 3 , m (z)) ′ and J κ 1 , κ 2 κ 3 , m (z) = (z 2) 2 κ 1 + κ 2 ∑ n = 0 ∞ (− 1) n Γ m (n + κ 1 + 1) Γ (n κ 3 + κ 1 + κ 2 + 1) (z 2) 2 n , was previously introduced and some of its geometric properties have been considered. In this paper, we report conditions for J κ 1 , κ 2 κ 3 , m (z) to be starlike and convex of order α, 0 ≤ α < 1 , inside the open unit disk using some technical manipulations of the gamma and digamma functions, as well as inequality for the digamma function that has been proved (Guo and Qi in Proc. Am. Math. Soc. 141(3):1007–1015, 2013). In addition, a method presented by Lorch (J. Approx. Theory 40(2):115–120 1984) and further developed by Laforgia (Math. Compet. 42(166):597–600 1984) is applied to establish firstly sharp inequalities for the shifted factorial that will be used to obtain the order of starlikeness and convexity. We compare then the obtained orders of starlikeness and convexity with some important consequences in the literature as well as the results proposed by all techniques to demonstrate the accuracy of our approach. Ultimately, a lemma by (Fejér in Acta Litt. Sci. 8:89–115 1936) is used to prove that the modified form of the function J κ 1 , κ 2 κ 3 , m (z) defined by I κ 1 , κ 2 κ 3 , m (z) = J κ 1 , κ 2 κ 3 , m (z) ∗ z / (1 + z) is in the class of starlike and convex functions, respectively. Further work regarding the function J κ 1 , κ 2 κ 3 , m (z) is underway and will be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]

In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over R n known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q ˙ -calculus and majorized l-tuples. Firstly we derive q ˙ -Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer's inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q ˙ -differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q ˙ -identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper. [ABSTRACT FROM AUTHOR]

A similar problem was recently considered with (t) (is the maximum value for the existence or no existence of), and. In this paper, we study same the equation (with) and we establish the existence of solutions satisfying the boundary conditions (0) (0) and (+). In order to do that, we utilize the shooting technique, then we consider the initial value problem consisting of the differential equation such that... and... We accompany our results by some numerical illustrations.. [ABSTRACT FROM AUTHOR]

The concept of convex ordered hyperrings associated with a strongly regular relation was investigated in this study. In this paper, we first studied hyperatom elements of ordered hyperrings and then investigated characterizations of quotient ordered rings. Is there a strongly regular relation θ on a convex ordered hyperring R for which R / θ is a convex ordered ring? This leads to an ordered ring obtained from an ordered hyperring. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to analyze the Montgomery identities and Ostrowski like inequalities, within the framework of quantum calculus. The study utilizes qϖ3 and qϖ4 differentiable functions to establish two new Montgomery identities, which are essential for the development of our main results which are new quantum estimates of general Ostrowski type inequality. The study involves numerous techniques, including q-identities, Hölder-like inequalities, and the Jensen-Mercer inequality for convex mappings, to derive the main outcomes of the paper. Additionally, the study presents special cases, numerical validation, and graphical illustrations to support the main results.

C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, probabilistic, quantum) inside categories of C*-algebras. At first, this paper concentrates on the commutative case and shows that there are functors from several Kleisli categories, of monads that are relevant to model probabilistic computations, to categories of C*-algebras. This yields a new probabilistic version of Gelfand duality, involving the "Radon" monad on the category of compact Hausdorff spaces. We then show that the state space functor from C*-algebras to Eilenberg-Moore algebras of the Radon monad is full and faithful. This allows us to obtain an appropriately commuting state-and-effect triangle for C*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we derive two new identities involving q-Riemann-Liouville fractional integrals. Using these identities, as auxiliary results, we derive some new q-fractional estimates of trapezoidal-like inequalities, essentially using the class of generalized exponential convex functions. [ABSTRACT FROM AUTHOR]

In the paper, we introduce subclasses of meromorphic functions by using principle of subordination and find necessary and sufficient condition for coefficients of functions F to belonge to these classes. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to analyze the Montgomery identities and Ostrowski like inequalities, within the framework of quantum calculus. The study utilizes q ϖ 3 and q ϖ 4 differentiable functions to establish two new Montgomery identities, which are essential for the development of our main results which are new quantum estimates of general Ostrowski type inequality. The study involves numerous techniques, including q -identities, Hölder-like inequalities, and the Jensen-Mercer inequality for convex mappings, to derive the main outcomes of the paper. Additionally, the study presents special cases, numerical validation, and graphical illustrations to support the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a distributed optimization problem of minimizing sum of convex functions over the intersection of fixed-point constraints. We propose a distributed method for solving the problem. We prove the convergence of the generated sequence to the solution of the problem under certain assumption. We further discuss the convergence rate with an appropriate positive stepsize. A numerical experiment is given to show the effectiveness of the obtained theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we would like to state well-known Ostrowski inequality via generalized Montgomery identity for the Φ - λ -convex function. Also, we would like to state the generalization of the classical Ostrowski inequality via generalized fractional integrals, which is obtained for functions whose first derivative in absolute values is Φ - λ -convex. Moreover we establish some Ostrowski type inequalities via generalized fractional integrals and their particular cases for the class of functions whose derivatives in absolute values at certain powers are Φ - λ - convex by using different techniques including Hölder's inequality and power mean inequality. Also, standard results would be capture as special cases. Moreover, some applications in terms of special means would also be given. [ABSTRACT FROM AUTHOR]

This paper introduces the stochastic Fejér-monotone hybrid steepest descent method (S-FM-HSDM) to solve affinely constrained and composite convex minimization tasks. The minimization task is not known exactly; noise contaminates the information about the composite loss function and the affine constraints. S-FM-HSDM generates sequences of random variables that, under certain conditions and with respect to a probability space, converge point-wise to solutions of the noiseless minimization task. S-FM-HSDM enjoys desirable attributes of optimization techniques such as splitting of variables and constant step size (learning rate). Furthermore, it provides a novel way of exploiting the information about the affine constraints via fixed-point sets of appropriate nonexpansive mappings. Among the offsprings of S-FM-HSDM, the hierarchical recursive least squares (HRLS) takes advantage of S-FM-HSDM's versatility toward affine constraints and offers a novel twist to LS by generating sequences of estimates that converge to solutions of a hierarchical optimization task: minimize a convex loss over the set of minimizers of the ensemble LS loss. Numerical tests on a sparsity-aware LS task show that HRLS compares favorably to several state-of-the-art convex, as well as non-convex, stochastic-approximation, and online-learning counterparts. [ABSTRACT FROM AUTHOR]

In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy's inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

We consider univalent functions, analytic in the unit disc |z| < 1 in the complex plane C which map |z| < 1 onto a domain with some nice property. The purpose of this paper is to find some new conditions for strong starlikeness and some related results. [ABSTRACT FROM AUTHOR]

The negative stiffness (NS) phenomenon and additional supplemental damping (AD) were proposed and investigated in recent years. Despite the bulk of literature on the base shear reduction for structures with the NS at the base or on the first story, the application of the NS and AD in the stories of a superstructure was barely studied. Considering the implementation of the NS and AD in a passive way, this paper proposes an innovative approach to optimize the NS and AD values on the different stories of civil structures. First, the formulation is derived to convert the optimization of NS and AD to the static feedback decentralized controller design problem. Then, the controller is searched by homotopy path, which leads to a local optimal solution. Finally, the procedure is validated by a 20-story benchmark structural model. [ABSTRACT FROM AUTHOR]

Let ${\mathcal{S}}$ denote the set of all univalent analytic functions $f$ of the form $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$ on the unit disk $z<1$. In 1946, Friedman [‘Two theorems on Schlicht functions’, Duke Math. J.13 (1946), 171–177] found that the set ${\mathcal{S}}_{\mathbb{Z}}$ of those functions in ${\mathcal{S}}$ which have integer coefficients consists of only nine functions. In a recent paper, Hiranuma and Sugawa [‘Univalent functions with half-integer coefficients’, Comput. Methods Funct. Theory13(1) (2013), 133–151] proved that the similar set obtained for functions with half-integer coefficients consists of only 21 functions; that is, 12 more functions in addition to these nine functions of Friedman from the set ${\mathcal{S}}_{\mathbb{Z}}$. In this paper, we determine the class of all normalized sense-preserving univalent harmonic mappings $f$ on the unit disk with half-integer coefficients for the analytic and co-analytic parts of $f$. It is surprising to see that there are only 27 functions out of which only six functions in this class are not conformal. This settles the recent conjecture of the authors. We also prove a general result, which leads to a new conjecture. [ABSTRACT FROM AUTHOR]

The thesis of this paper is that when the indifference curve is concave to the origin, the optimal point on the budget line is not the corner solution on the highest (most north eastern) indifference curve, the analysis all too often offered in the literature, but, rather, somewhat paradoxically, the lowest (most south western) indifference curve. The economics profession, as articulated through the megaphone of intermediate micro economics texts, offers a mixed result in this regard. Some few do offer a correct analysis, but many do not; others ignore the issue entirely. The contribution of the present paper and the aim of our research is to provide a correction of the widespread but erroneous indifference curve analysis that appears in many of our intermediate microeconomics texts. Our methodology is one of contrast: we offer what we see as both the correct and the incorrect versions of indifference curve analysis. [ABSTRACT FROM AUTHOR]

The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function J λ , μ ν , m (z) : = Γ m (λ + 1) Γ (λ + μ + 1) 2 2 λ + μ z 1 − (ν / 2) − λ J λ , μ ν , m (z) , where the function J λ , μ ν , m satisfies the differential equation J λ , μ ν , m (z) : = (1 − 2 λ − ν) J λ , μ ν , m (z) + z (J λ , μ ν , m (z)) ′ with J ν , λ μ , m (z) = (z 2) 2 λ + ν ∑ k = 0 ∞ (− 1) k Γ m (k + λ + 1) Γ (k μ + ν + λ + 1) (z 2) 2 k for λ ∈ C ∖ Z − , Z − : = { − 1 , − 2 , − 3 , ... } , m ∈ N , ν ∈ C , and μ ∈ N 0 : = N ∪ { 0 } . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, 0 ≤ α < 1 . Ultimately, we discuss the starlikeness and convexity of order zero for J λ , μ ν , m , and it turns out that they are useful to extend the range of validity for the parameter λ to λ ≥ 0 where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates. [ABSTRACT FROM AUTHOR]

Abstract The main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and χ κ $\chi _{{\kappa }}$ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of χ κ $\chi _{{\kappa }}$ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over Rn known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q˙-calculus and majorized l-tuples. Firstly we derive q˙-Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer’s inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q˙-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q˙-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper.

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0,π). We find bounds for |fz(z)|, and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction. [ABSTRACT FROM AUTHOR]

In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.

Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young's inequality, Hölder's inequality, Minkowski's inequality, Hermite–Hadamard's inequality, Ostrowski's inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard's inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals. [ABSTRACT FROM AUTHOR]

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V|³) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree. [ABSTRACT FROM AUTHOR]

High-quality convex colloidal photonic crystals can be grown on the tip of an optical fiber by self-assembly using the hanging drop method. They are convex-shaped, produce the diffraction of reflecting light with high efficiency (blazing colors), and have a high curvature. The convex colloidal crystals are easily detachable and, as free-standing objects, they are mechanically robust, allowing their manipulation and use as convex reflective diffraction devices in imaging spectrometers. Currently, the same characteristics are obtained by using gratings-based structures. The optical fiber/colloidal crystal interface is disordered; thus, no light diffraction can be registered. The ordering at this interface was highly increased by forming a polystyrene spacer on the optical fiber tip, which served as a self-assembly substrate for silica colloid, as a mechanical bond between the fiber and the crystal, and as a filler reservoir for an inverse-opal synthesis. The silica opal-like grown on the optical fiber tip can be transformed into a high-quality polystyrene (blazing colors) inverse-opal by using the polystyrene spacer as a filler. We found that the colloidal crystal axisymmetric self-assembles onto the optical fiber tip only if a maximum volume of the colloid drop is settled on a flat end of the polystyrene spacer. [ABSTRACT FROM AUTHOR]

In this paper, we derive some Hermite-Hadamard type inequalities via s-convex functions of first and second sense respectively. These inequalities involve k-Riemann-Liouville fractional integrals. We also discuss some special cases. [ABSTRACT FROM AUTHOR]

Researches in "point-free geometry", aiming to found geometry without using points as primitive entities, have always paid attention only to the logical aspects. In this paper, we propose a point-free axiomatization of geometry taking into account not only the logical value of this approach but also, for the first time, its educational potentialities. We introduce primitive entities and axioms, as a sort of theoretical guise that is grafted onto intuition, looking at the educational value of the deriving theory. In our approach the notions of convexity and half-planes play a crucial role. Indeed, starting from the Boolean algebra of regular closed subsets of ℝn, representing, in an excellent natural way, the idea of region, we introduce an n-dimensional prototype of point-free geometry by using the primitive notion of convexity. This enable us to define Re-half-planes, Re-lines, Re-points, polygons, and to introduce axioms making not only meaningful all the given definitions but also providing adequate tools from a didactic point of view. The result is a theory, or a seed of theory, suitable to improve the teaching and the learning of geometry. [ABSTRACT FROM AUTHOR]

The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of $ {\mathfrak{q}} $-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the $ _{{\varsigma_{1}}}{\mathfrak{q}} $ and $ ^{{{\varsigma_{2}}}}{\mathfrak{q}} $ differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint $ {\mathfrak{q}} $-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations.

The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed in a sigma-semiring in a NHC under a topological ordering of NHCs. The topological ordering relation maintains the irreflexive and anti-symmetric algebraic properties while retaining the homeomorphism of NHCs. The monotonic measure sequence in a NHC determines the convexity and compactness of topological subspaces. Interestingly, the topological ordering in NHCs in two isomorphic topological spaces induces the corresponding ordering of measures in sigma-semirings. Moreover, the uniform topological measure spaces of NHCs need not always preserve the pushforward measures, and a NHC semiring is functionally separable by a set of inner-measurable functions. [ABSTRACT FROM AUTHOR]

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p=2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles.

The purpose of this paper is to introduce some characterizations of (Gaussian) hypergeometric function to be in various subclasses of uniformly starlike and uniformly convex functions. Operators related to hypergeometric functions are also considered. Some of our results correct previously known results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide a result which concerns with the boundary behavior of analytic functions. It may be a local version of the well known Jack's lemma when we change the function normalization at the origin. [ABSTRACT FROM AUTHOR]