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For a simple, finite, and connected graph G, the spherical maximal operator is defined as ... where ... is the sphere with center at t and having radius r. In this paper, we consider the spherical maximal operator ... on ... spaces and calculate the ... for ... and estimate the ... for ..., when G is Km. Furthermore, We establish the maximum and minimum bounds for the spherical maximum operator on finite graphs and indicate the graphs that achieve these bounds. [ABSTRACT FROM AUTHOR]

The sixth paper, "On Some New Ostrowski-Mercer-Type Inequalities for Differentiable Functions", by Sial et al. [[6]], establishes a new integral identity involving differentiable functions and uses it for some new Ostrowski-Mercer-type inequalities for differentiable convex functions. The importance of inequalities in Mathematics is beautifully summarized in a citation attributed to Respected Professor Andrey Nikolaevich Kolmogorov: HT

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]

Motivated by recent investigations relating the sharpness of the Jensen inequality, this paper concerns with the sharpness of the converse of the Jensen inequality. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. In this Special Issue, we present new results related to classical inequalities, such as the Jensen inequality, Jensen-Steffensen inequality, Jessen inequality, Grüss inequality, Chebyshev inequality, etc. [Extracted from the article]

In this paper, we investigate the effect of dependent errors in the fixed design nonparametric regression models. Under some mild conditions, we obtain the complete consistency and asymptotic normality for the weighted estimator in the fixed design nonparametric regression models. In addition, a simulation study is undertaken to investigate finite sample behavior of the estimator. [ABSTRACT FROM AUTHOR]

The ordering betweenWigner-Yanase-Dyson function and logarithmic mean is known. Also bounds for logarithmic mean are known. In this paper, we give two reverse inequalities for Wigner-Yanase-Dyson function and logarithmic mean. We also compare the obtained results with the known bounds of the logarithmic mean. Finally, we give operator inequalities based on the obtained results. [ABSTRACT FROM AUTHOR]

Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros be 0. In this paper, we investigate the relative growth of a polynomial p(z) with respect to two circles z=r and z = R and obtain inequalities about the dependence of p(rz) on p(Rz), where z = 1, for 0 while taking into account the placement of the zeros of the underlying polynomial. Our results improve as well as generalize certain well-known polynomial inequalities. Some numerical examples are also given in order to illustrate and compare graphically the obtained inequalities with some recent results. [ABSTRACT FROM AUTHOR]

Let Q be a bounded domain of RN (Nx1) with boundary of class C2. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms established in [8]. As weights we treat non-doubling functions of the distance to the boundary . [ABSTRACT FROM AUTHOR]

In this paper we provide new refinements of Aczel-type inequality and give some applications. Furthermore, we show that two of three theorems in the work by J. Tian and M.-H. Ha (J. Math. Inequal. 12 (1) (2018), 175-189) are incorrect whereas the proof of the other is technically wrong. We establish an improvement of the correctly stated theorem with a simple proof and give counterexamples to the wrong ones. [ABSTRACT FROM AUTHOR]

The concept of convexity of functions is a useful instrument that is used to solve a wide range of pure and applied scientific issues. The Hermite-Hadamard inequality which is also used frequently in many other parts of practical mathematics notably in optimization and probability is one of the most important mathematical inequalities relevant to convex maps. The fractional calculus, a calculus of non-integer order has applications in diverse fields of physical sciences. In this paper, we have established Hermite-Hadamard's inequalities via Riemann-Liouville fractional integral for the case of harmonically convex function as well as the products of two harmonically convex functions via Riemann-Liouville fractional integrals. [ABSTRACT FROM AUTHOR]

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1 ≪ L ≲ N . A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N → ∞ , then an asymptotic analysis of the entanglement entropy as L → ∞ . In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L → ∞ , N → ∞ , L / N → λ > 0 . Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula. [ABSTRACT FROM AUTHOR]

Let A be a bounded positive operator on a complex Hilbert space ... . The semi-product ..., induces a semi-norm ... on H. Let ωA (T) amd ... denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space ..., respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-inner product space induced by A are derived. In particular, for ... and α ≥ 0, we prove that ... and ... . It is worth noting that our results improve the existing A-numerical radius inequalities. Further, we also give a refinement inequality of A-operator semi-norm triangle inequality. [ABSTRACT FROM AUTHOR]

Let ... be a polynomial of degree n having all its zeros in ..., then Aziz [Proc. Am. Math. Soc., 89, (1983) 259--266] proved ... . In this paper, we prove a polar derivative extension which sharpens the above inequality. As a consequence, we also derive a result on Bernstein type inequality for the class of polynomials having all its zeros in ... . [ABSTRACT FROM AUTHOR]

This paper establishes the mapping properties of the fractional integral operators on the grand Morrey spaces and the grand Hardy-Morrey spaces defined on the Euclidean spaces. We obtain our results by refining the Rubio de Francia extrapolation method as the existing extrapolation method cannot be directly applied to the grand Morrey spaces. This method also yields the mapping properties of nonlinear operators. In particular, we establish the Sobolev embedding, the Poincaré inequality and the mapping properties of the fractional geometric maximal functions on the grand Morrey spaces. [ABSTRACT FROM AUTHOR]

The paper is focused on two-sided splitting inequalities for differences of complex exponentials ... for large ... is real unbounded sequence clustering with appropriate speed. Moreover, it is shown that if ... is a Riesz basis of a Hilbert space H, then for any k ≥ 1 the system ... is complete, minimal but not uniformly minimal in H. Also some properties of systems of functions of real argument t, ... where ..., are discussed. [ABSTRACT FROM AUTHOR]

Let ... and t, r, p ∈ (0, ∞) . In this paper, we introduce the slice Besov-type space ... and the slice Triebel-Lizorkin-type space ..., and establish their φ-transform characterizations in the sense of Frazier and Jawerth. The embedding properties, characterizations via the Peetre maximal function, the Lusin area function, smooth atomic and molecular decompositions of these spaces are also obtained. As applications, we obtain the boundedness on these spaces of Fourier multipliers with symbols satisfying some generalized Hörmander condition. [ABSTRACT FROM AUTHOR]

We in this paper improve the well-known C. R. Johnson's lower bound for the smallest singular value via permutation matrices. A direct algorithm is also given to compute the new lower bound. [ABSTRACT FROM AUTHOR]

In this paper we provide several upper and lower bounds for the Ostrowski difference ... where f : C → R is a convex function, C is a convex subset of a vector space X and w is integrable and nonnegative a.e. on [0,1] . A perturbed version under some natural assumptions on the weight function w is also considered. These results are then employed to obtain several weighted integral inequalities for norms and semi-inner products. The particular case of inner product spaces is analyzed and refinements of the weighted integral midpoint inequality for norms are provided. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Baskakov-type operator. Firstly, we obtain the rate of convergence by using modulus of continuity and then Voronovskaja type asymptotic formula for these operators. [ABSTRACT FROM AUTHOR]

In this paper, we give some new improvements and reverse improvements of Young type inequalities. The conclusion proved by Yang and Wang [J. Math. Inequal., 17 (2023), 205-217] involved the monotonicity of ..., where ... and ... . This article demonstrates the monotonicity of ..., where ... and ... . And this implies a main conclusion as follows: ..., where ... and ... . Furthermore, we can get some related results about operator, Hilbert-Schmidt norm, trace norm by these scalars results. [ABSTRACT FROM AUTHOR]

In this paper, we give some characterizations for the boundedness and compactness of some Stević-Sharma type operators called the polynomial differentiation composition operators from H∞ into the Bloch space on the unit disk. [ABSTRACT FROM AUTHOR]

This paper is devoted to establishing frame inequalities in Hilbert spaces. By using operator theory methods, several two-sided inequalities for frames are presented, which, comparing to previous inequalities on frames and generalized frames, admit new structures. [ABSTRACT FROM AUTHOR]

In this paper, we present some properties of the time scale nabla calculus and how to apply it for proving the dynamic inequalities. Also, we prove some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus and also, we study the characterizations of the weights for these inequalities in different spaces and for the exponent p > 1. The Holder inequality, Jensen inequality, and Minkowski inequality are used to prove our results. [ABSTRACT FROM AUTHOR]

In this paper we obtain generalizations of Hardy-type inequalities for convex functions of the higher order by applying Hermite interpolating polynomials. The results for particular cases: Lagrange, (m,n-m) and two-point Taylor interpolating polynomials are also considered. Finally, we derive the Grüss and Ostrowski type inequalities related to these generalizations. [ABSTRACT FROM AUTHOR]

Abstract. This paper will introduce the theory of ϕ-Jensen coefficient. By means of the functional analysis, linear algebra, discrete mathematics and inequality theories with proper hypotheses, the Jensen-type inequality, Marshall-type inequality and the Ky Fan-type inequality are obtained as follows: ... respectively, as well as we also displayed the applications of our main results in business profit management model, and some conditions such that ... hold are obtained, where p is the profit function and e is the cost function. [ABSTRACT FROM AUTHOR]

In this paper, we study the Hyers–Ulam stability of Hadamard fractional Itô–Doob stochastic integral equations by using the Banach fixed point method and some mathematical inequalities. Finally, we exhibit three theoretical examples to apply our theory. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix. [ABSTRACT FROM AUTHOR]

This paper deals with a sharp version of mid-point type inequality in connection with fractional integrals of real valued absolutely continuous functions as a generalization and refinement of non-sharp classical mid-point inequality which is presented by the Riemann integrals of differentiable real valued functions whose derivative absolute values are convex. Some special functions, numerical means and a mid-point type formula are considered to discuss about some applications of main results. [ABSTRACT FROM AUTHOR]

This paper defines and studies the σ type mixed Morrey spaces. Furthermore, we introduce the predual spaces of σ type mixed Morrey spaces to establish the extrapolation theorem. As applications of extrapolation theory, we character the BMO space in different ways. On the one hand, we character the BMO spaces by the new John-Nirenberg inequality in terms of σ type mixed Morrey spaces. On the other hand, we establish the characterization of BMO spaces by the boundedness of commutators of the singular integral operator on σ type mixed Morrey spaces. [ABSTRACT FROM AUTHOR]

The authors investigate the complete moment convergence for arrays of rowwise independent random elements in Rademacher p Banach spaces. The results obtained in this paper improve the corresponding theorems of Hu et al. (Hu, T.-C., Rosalsky, A., Volodin, A., Zhang, S., 2021. A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type p Banach spaces. II, Stochastic Anal. Appl., 39 (1), 177-193). Some corollaries and examples are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some improvements and generalizations of Young's inequalities on the arithmetic, geometric, and harmonic mean. For example, In addition, we obtain some new results for Young's inequality for operators. [ABSTRACT FROM AUTHOR]

In this paper the extension of the weighted Montgomery identity is established by using the integral formula of Pecaric, Matic and Ujevc. Further, by using this extended weighted Montgomery identity for functions whose derivatives of order n-1 are absolutely continunous functions, new inequalities of the weighted Hermite-Hadamard type are obtained. Also, applications of these results are given for various types of weight function. [ABSTRACT FROM AUTHOR]

In this paper, we give several numerical radius inequalities for Hilbert space operators by using the Young-type inequalities and the generalization of the Buzano of the Schwarz inequality. These inequalities improve the classical numerical radius inequalities. We also give the upper bound of the numerical radius of 2x2 operator matrices. [ABSTRACT FROM AUTHOR]

This paper concerns the study singular integrals along twisted surfaces of the form We prove Lp bounds for the corresponding operators when the surfaces are defined by mappings more general than polynomials and convex functions, provided that the kernels are in L(logL)2(Sn-1x Sm-1) . [ABSTRACT FROM AUTHOR]

Integral inequalities are the proficient aspect of mathematical analysis. Various techniques have been deployed to acquire to fresh inequalities which are beneficial in various area problems. The aim of this paper is to derive some new analytic inequalities involving generalized weighted exponential beta functions. To attain our primary objectives, we introduce the generalized exponential function X and weighted form of exponential beta functions Furthermore, we briefly discuss their properties. we derive several inequalities in association with As the applications of these new developments,we conclude some error estimates of Ostrwoski's type inequalities, which show the significance of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonlinear higher-order Kirchhoff-type equation with dissipation in a bounded domain. By establishing a first order differential inequality technique, a lower bound for the blow-up time is obtained when the blow-up of solution occurs. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to prove several majorization type inequalities using Green and 4-convex functions. First of all, we drive generalized majorization inequality for arbitrary n-tuples and real weights. Further, we explore the inequality for majorized tuples, weighted majorization theorems given by Fuchs, Dragomir and Maligranda et al. For deriving another generalized majorization inequality, we use a simple form of Jensen's inequality, and by similar fashion we apply classical earlier majorization theorems for further elaborations of generalized inequality. Several applications of information theory are discussed at the end of the article. [ABSTRACT FROM AUTHOR]

Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper. [ABSTRACT FROM AUTHOR]

Let A,B,C ∈ Cn×n be positive semidefinite matrices and let |A|, |B|, |C| be determinants of A, B, C ∈ Cn×n respectively. In this paper, the authors prove two determinantal inequalities |A + B + C| + |C| ≥ |A + C| + |B + C| + (2n - 2) |AB|1/2 + 3(3n-1 - 2n + 1) |ABC|1/3 and |A + B + C| + |A| + |B| + |C| ≥ |A + B| + |A + C| + |B + C| + 3(3n-1 - 2n + 1)|ABC|1/3. These two inequalities refine known ones. [ABSTRACT FROM AUTHOR]

s t r i n g U t i l s. c o n v e r t A b s t r a c t M a t h H t m l (formulaUtilTools.convertMathHtml( s t r i n g U t i l s. c o n v e r t M m l (!article.abstractinfoEn)),'en') Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initial-boundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Hölder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Hölder continuity. [ABSTRACT FROM AUTHOR]

There exists a one to one correspondence between higher derivations {dn}n∞=0 on an algebra A and the family of sequences of derivations {δn}n=1∞ on A. In this paper, we obtain a relation that calculates each derivation δn(n ∈ N) directly as a linear combination of products of terms of the corresponding higher derivation {dn}n∞=0. Also, we find the general form of the family of inner derivations corresponding to an inner higher derivation. We show that for every two higher derivations on an algebra A, the product of them is a higher derivation on A. Also, we prove that the product of two inner higher derivations is an inner higher derivation. [ABSTRACT FROM AUTHOR]

Feature selection is one of the most important tasks in machine learning. Traditional feature selection methods are inadequate for reducing the dimensionality of online data streams because they assume that the feature space is fixed and every time a feature is added, the algorithm must be executed from the beginning, which in addition to not performing real-time processing, causes many unnecessary calculations and resource consumption. In many real-world applications such as weather forecasting, stock markets, clinical research, natural disasters, and vital-sign monitoring, the feature space changes dynamically, and feature streams are added to the data over time. Existing online streaming feature selection (OSFS) methods suffer from problems such as high computational complexity, long processing time, sensitivity to parameters, and failure to account for redundancy between features. In this paper, the process of OSFS is modeled as a multi-objective optimization problem for the first time. When a feature stream arrives, it is evaluated in the multi-objective space using fuzzy Pareto dominance, where three feature selection methods are considered as our objectives. Features are ranked according to their degree of dominance in the multi-objective space over other features. We proposed an effective method to select a minimum subset of features in a short time. Experiments were conducted using two classifiers and eight OSFS algorithms with real-world datasets. The results show that the proposed method selects a minimal subset of features in a reasonable time for all datasets. [ABSTRACT FROM AUTHOR]

One of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weights may reflect some additional characteristics of the events such as their relative importance. In this paper, Axiomatic derivations and properties of weighted exponential entropy parallel to those achieved for weighted entropy are investigated. The relation between weighted exponential entropy of X and a strictly monotone and nonnegative function of X has obtained. The generalized weighted entropy and the generalized weighted exponential entropy for continuous random variable have been presented. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to prove the existence and uniqueness of mild solution for abstract differential equations by using the resolvent operators and fixed point theorem. Moreover, we studied some examples on partial differential equation with Caputo-Fabrizio derivative. [ABSTRACT FROM AUTHOR]

This paper exploits non-autonomous Caputo-type systems associated with unbounded delayed arguments. We formulate a new theorem and provide proof that gives limiting behaviour of nontrivial solutions to zero vector. Two examples are provided to illustrate the proposed theorem. [ABSTRACT FROM AUTHOR]

In the paper, we establish two inequalities for differentiable bounded functions and Lipschitzian function, which are connected with Iyengar integral inequalities, and we present some new results. [ABSTRACT FROM AUTHOR]

This paper presents the first investigation of extended dissipative synchronization in a specific type of Takagi-Sugeno (T-S) fuzzy complex dynamical networks with interval hybrid coupling delays. First, the decoupling method is employed to reorganize the multiple communication dynamical system, which comprises discrete-time, partial and distributed coupling delays. Second, the non-fragile control, which allows for uncertainty management within predefined norm bounds, has been applied to networks. Moreover, it becomes possible to derive a less conservative condition by utilizing multiple integral Lyapunov functionals, a decoupling strategy, Jensen's inequality, Wirtinger's inequality, and mathematical inequality techniques. This condition ensures that the T-S fuzzy complex dynamical networks, with interval hybrid coupling delays, can attain asymptotic synchronization with the assistance of a non-fragile feedback controller. Additionally, we extended this system to the extended dissipativity analysis, including passivity, L2 - L∞, H∞ and dissipativity performance in a unified formulation. A set of strict linear matrix inequalities (LMIs) conditions is a sufficient criterion. Finally, two simulation examples are proposed to verify the merit of the obtained results. [ABSTRACT FROM AUTHOR]

The study of convex functions occupied and still occupies a central role in Inequalities Theory because the convex functions develop a series of inequalities. The newly established identity is then used to show some new Simpson's formula type inequalities for HT ht -differentiable convex functions. For example, the study of convex functions has occupied a central role in the theory of inequalities because such functions develop a series of inequalities. The theory of inequalities represents a long-standing topic in many mathematical areas and remains an attractive research domain with many applications. [Extracted from the article]

Exponential function is one of the most important functions in mathematics and is helpful in theoretical investigations and practical applications. For example, exponential functions are the solutions to the simplest types of dynamical systems. In particular, an exponential function arises in simple models of bacterial growth, it can describe growth or decay, etc. The main purpose of this paper is one exponential inequality, which arose in the study of the properties of exponential functions. [ABSTRACT FROM AUTHOR]

This paper investigates the cavity–magnon steering and qubit–qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity–magnon steering and qubit–qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom–field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon–field coupling enhances and elevates the lower bounds of qubit–qubit steering. Further, adding the damping rates causes deterioration of the cavity–magnon steering and qubit–qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters. [ABSTRACT FROM AUTHOR]