In this paper, we study the distribution of Fourier coefficients of triple product L-functions associated with certain GL(6) automorphic forms. More precisely, we derive asymptotic formulas for the first moment of Fourier coefficients of the automorphic L-functions attached to these GL(6) forms. As an application, we derive subconvexity bounds for the associated L-functions on the critical line.
We prove a fractional Hermite-Hadamard-Mercer inequality via psi-Hilfer integral operators for the class of h-convex functions, where h is a B-function. Some novel fractional inequalities related to the left and right sides of the Hermite-Hadamard-Mercer inequalities are established for differentiable mappings whose absolute values of the derivatives are h-convex. Moreover, we construct new inequalities for these differentiable functions using Holder's inequality.
This paper investigates mappings with Istrat & cedil;escu type contractive properties within the framework of new extended b-metric spaces. Various generalized contractive operators are defined, including those of order 2, two-sided, type 2, and Ciric-convex contractions. The study establishes several fixed point theorems for these mappings under specific conditions, such as orbital continuity or the boundedness of the function involved in the structure of the new extended b-metric space. These results extend previous findings in the literature.
We establish a Korovkin-type theorem for sublinear operators in the framework of modular spaces by using statistical convergence and provide an illustrative example demonstrating its applicability.
Numerous generalizations of the rudimentary concept of hypergroups have been explored since its introduction by Marty. In this paper, we consider a notable category of non-associative cyclic hyperstructures called single power cyclic LA-hypergroups which are a conception of cyclic hypergroups and LA-semigroups. We enumerate single power cyclic LA-hypergroups of order two (and three) and period two. Additionally, we investigate some features of these single power cyclic LA-hypergroups. We also study various properties of cyclic LA-hypergroups and examine the differences between cyclic groups and cyclic LA-hypergroups.
The paper aims to investigate an alternative form of multi-Euler-Lagrange-cubic mappings. We provide a characterization of multi-Euler-Lagrange cubic mappings and multi-Euler-Lagrange-Jensencubic mappings by unifying the corresponding systems of equations into a single defining equation. We investigate the Hyers-Ulam stability for multi-Euler-Lagrange-Jensencubic mappings by applying a fixedpoint method in Banach spaces. Also, we deduce several other results corresponding to well-known stability results, and provide a suitable counterexample to demonstrate a failure case of stability.
Let H denote the Hamiltonian Lie superalgebra H(m, n; t) over a field of characteristic p >= 3, which has a finite Z-grading structure. In this paper, we take a canonical torus T-H of H, which is an abelian subalgebra of H. By the decomposition of the weight space of H with respect to T-H, we show the action of the unique linear map related to the symmetric super-biderivation on the elements of the generators of H. Moreover, we prove that each symmetric super-biderivation of H is zero. Further, we get that each super-biderivation of H is inner. As applications, the super-commutative post-Lie superalgebra structures and the linear super-commuting maps on H are described.
In this paper, the controllability of Hilfer fractional neutral stochastic impulsive differential equations with integral impulses is investigated. The controllability result is established through the application of semigroup of operators, measure of noncompactness, Monch's fixed point theorem, and stochastic analysis techniques. An example is presented to validate the theoretical findings.
Since few last decades, a number of researchers have been working on wavelet methods and on approximation of functions with bounded derivatives in various function spaces. But they investigated the function f E L-2 [0, 1) whose either first, second, third or fourth derivative is bounded. Their results did not give any idea about a function whose fifth or higher order derivative is bounded. Therefore in present investigation we have taken a function f E L-2 [0,1) whose fifth and mth order derivative is bounded and found their error estimation by using Legendre wavelet method. In this paper, we have established two new theorems on wavelet approximation of a function f with 0 < I f(o)v(t)I
The purpose of this paper is to give new sequence spaces derived from derangement numbers. Also, we investigate their topological properties such as Schauder basis, the beta-duals as well as characterization of certain matrix operators. Furthermore, by means of Hausdorff measure of noncompactness, we present the characterization of some compact operators.
One of the most classical spectral Turan problems is determining the maximum spectral radius of triangle-free graphs and hypergraphs. As the hypergraph analogue of triangles, Fan(k) is a linear k-uniform hypergraph with k hyperedges f(1), . . . , f(k) which pairwise intersect in a common vertex v, and an additional hyperedge g which intersects all f(i) in a vertex different from v. Let K-s,t(-) be the graph obtained from a complete bipartite graph K-s,K-t by deleting an edge. Motivated by the classic theorems on triangle-free graphs due to Erdos and Nosal, and by the Turan number of Fan(k) on linear k-uniform hypergraphs determined by Furedi and Gyarfas respectively, we prove that rho(G) <= rho(K-[n/2],[n/2](-)) where rho(G) is the spectral radius of a connected triangle-free graph G with order n and diameter 3, and spex(k )(lin)(m, Fan(k)) = root m where spex(k )(lin)(m, Fan(k)) denotes the maximum spectral radius of Fan(k)-free linear k-uniform hypergraphs with size m.
The classical estimator for the estimation of the finite population mean in the presence of non-response is the Hansen-Hurwitz estimator. This study first examines the use of ranked set sampling in the Hansen-Hurwitz estimator for both response and non-response groups. Subsequently, a new estimator is proposed by employing median ranked set sampling for the same estimator. The sample selection is performed using the median ranked set sampling method for both response and non-response groups. A simulation study is conducted to investigate the efficiency of the estimators under different distributions, sample sizes, and subsample proportions, considering cases with perfect ranking and imperfect ranking. The obtained results are compared with various estimators available in the literature. Under unimodal symmetric distributions such as, Laplace and Normal distributions, the estimator based on the median ranked set sampling yields more efficient results, whereas under Uniform and Exponential distributions, the estimator based on the ranked set sampling is found to be more efficient. Moreover, the efficiency of the proposed estimator has been evaluated using real-life data. The proposed estimator has been found to produce more efficient results compared to other estimators in the presence of non-response.
An analytic function f (z) = z + a(2)z2 + & centerdot;& centerdot;& centerdot; defined on the unit disc D is close-to-starlike if there exists a starlike function g : D -> C satisfying the inequality Re(f(z)/g(z)) > 0 for all z is an element of D. We are particularly interested in the starlikeness of the class W, which consists of all functions that satisfy the close-to-starlike condition with g(z) equivalent to z and the subclass Wn of W, which contains all those functions of the form f (z) = z + a(n)+1z(n+1) + & centerdot;& centerdot;& centerdot;. The usual starlikeness of an analytic function f requires that the range of zf '(z)/ f (z) is contained in the right half-plane. More generally, a normalized analytic function f : D -> C is Ma-Minda starlike if the function z f '/ f is subordinate to the function phi and Ma-Minda convex if the function 1 + zf ''/ f ' is subordinate to the function phi. We have determined the sharp radius of Ma-Minda convexity/starlikeness of the class W and W(n)when the range of phi is a nephroid, lune, lemniscate of Bernoulli, cardioid, or, a particular rational function.
Zolezzi introduced the notion of well-posedness by perturbations for the minimization problem. In this paper, we extend this concept to Levitin-Polyak alpha-well-posedness by perturbations for split quasiequilibrium problems in real Banach spaces. We establish some metric characterization results between the (generalized) alpha-well-posedness by perturbations for split quasi-equilibrium problems and their solution set with the help of Kuratowski's measure of non-compactness. Moreover, we derive some conditions under which the alpha-well-posedness by perturbations of a split quasi-equilibrium problem is equivalent to the existence and uniqueness of its solution.
Dendriform algebras can be regarded as associative algebras whose product is decomposed into two operations satisfying some laws of dendriform algebra, which together form the associative law of the undecomposed associative algebra. We introduce a cohomology theory for dendriform algebras equipped with derivations and show the deformation theory is controlled by the cohomology and the collection of equivalence classes of abelian extensions is given by the second cohomology.
Radii of convexity and starlikeness provide significant insights into the geometric propertiesfor analytic functionsfdefined in the open unit diskDof the complex plane. It is well-known that iff(D) is a convex or a starlike domain, thenf(|z|
The literature has introduced several extensions of Shannon function entropy, including the Sharma-Taneja-Mittal entropy and its extensions. This paper presents new findings related to the survival cumulative Sharma-Taneja-Mittal entropy measure, including bounds, convergence, equivalent expressions, normalized survival cumulative Sharma-Taneja-Mittal entropy, its relationship with differential entropy, stochastic comparisons, and the excess wealth transform involving this measure. Additionally, the paper addresses the challenge of estimating the survival cumulative Sharma-Taneja-Mittal entropy using the empirical cumulative distribution function. Moreover, this entropy measure is estimated using two distinct empirical estimators of the cumulative distribution function. In addition, the measure is used to assess test uniformity, yielding an approximation of the distribution of the test statistic as well as the derivation of the limit distribution. The study also contains a simulation study to evaluate the power of the suggested test with other uniformity tests, and it covers the percentage points and power versus seven different distributions for this test statistic.
By employing the Laplace transform for Banach-space-valued functions, in this paper we evaluate the sums of some hyperharmonic-like series in Banach algebras and modules. We discuss the cases when the general terms of the given series are invertible in the respective algebras, and when they are invertible in the Drazin-Koliha sense, or the Mary-Patr & imath;cio sense. Afterwards, we extend our results to the multilateral modular series of the form (infinity)Sigma(k=1) (a(1) + k)(-n)(1) c(1)(a(2) + k)(-n)(2)c(2)& centerdot; . . . (a(m-)1 + k)(-n)(m-1) c(m-1)(a(m) + k)(-n)(m), where a(i) belong to possibly different Banach algebras, c(j) belong to possibly different Banach bimodules, and n(1), . . . , n(m) are positive integers. As an application, we obtain a new necessary solvability condition for the Sylvester equation ax - xb = c in Banach bimodules.
In this paper, we investigate a generalized Szasz-type positive linear operator recently introduced in the literature and analyze its fundamental properties through the study of moments. In particular, we construct several important modifications, namely the Stancu, Kantorovich and Stancu-Kantorovich variants, and derive explicit expressions for their first-and second-order moments. These moment identities provide the basis for establishing various approximation properties of the operators. More specifically, they are instrumental in proving Korovkin-type theorems, estimating rates of convergence via the modulus of continuity and Peetre's K-functional, and examining approximation behavior in Lipschitz spaces. Furthermore, we employ these identities to obtain Voronovskaya-type asymptotic results. The findings presented here contribute to a deeper understanding of the approximation capabilities of generalized Szasz-type operators and their modifications, thereby enriching the theory of positive linear operators.
This paper investigates the gDMP inverse of generalized Drazin invertible operators with closed range. Several characterizations and properties of the gDMP inverse are established. Furthermore, key properties are derived, and applications to the solution of certain linear operator equations are presented.
