In this paper, we establish some lower bound estimates for a certain class of rational functions on a disk with prescribed poles and restricted zeros. The results obtained strengthen some known results for rational functions and in turn produce generalizations of some polynomial inequalities as well.
In this manuscript, we present a collection of inequalities that extend and generalize the important results of the findings from [14], with the latter serving as specific cases within our study. Our research takes many forms of fractional differential inequalities, including the comprehensive structure of the Caputo fractional derivative operator with respect to a function . Furthermore, we demonstrate the practical applications of a--convex functions in the domain of fractional calculus within this framework.
In this paper, singularly perturbed time-fractional parabolic reactiondiffusion of initial boundary value problem is studied. The time-fractional derivative is applied in the Caputo fractional sense and handled by implicit Euler method. The spatial derivative is approximated by fitted cubic B-spline collocation method on a uniform mesh. Convergence analysis of the scheme is conducted and it is accurate of order O(h(2) + (triangle t(2-alpha))). To test the effectiveness of proposed method two model examples are considered. The results from the experiment confirm that the scheme is uniformly convergent and has twin layers at the end spatial domain.
We obtain the celebrated Hardy's inequality in the context of variable exponent sequence spaces.
A new geometric background of graph invariants was introduced by Gutman, of which the simplest is the second Somb or index SO2, defined as SO2 = SO2(G) =& sum;(uv is an element of E)|d(2)G(u)-d(2)G(v)| / d(2)G(u)+d(2)G(v), where G = (V, E) is a simple graph and d(G)(v) denotes the degree of v in G. In this paper, the chemical applicability of the second Somb or index is investigated and it is shown that the second Somb or index is useful in predicting physicochemical properties with high accuracy compared to some well-established and often used indices. Also, we obtain a bound for the second Somb or index among all (molecular) trees with fixed numbers of vertices, and characterize those molecular trees achieving the extremal value.
In this paper, we study and investigate unified and extended fractional integral operator involving the multivariable I-function defined by Prasad, Raizada's generalized polynomial set and general class of multivariable polynomials. During the present study, we derive five theorems pertaining to Mellin transforms of these operators. Furthermore, on account of the general nature of the functions involved herein, many known and (presumably) new fractional integral operators involved simpler functions can be obtained. We also give the special case concerning the multivariable H-function.
In this paper, our focus is on a specific class of non-linear psi-Hilfer fractional generalized double phase-Choquard differential equations involving the p-Laplacian operator with Dirichlet boundary conditions. The equation is given by: {L(gamma,beta;psi)u = (integral(ohm)G(u(x))/|x-y|(lambda )dx) g(u(y)), in ohm, u = 0, on partial derivative Omega, with L(gamma,beta;psi )is defined as: L(gamma,beta;psi)u := D-T(gamma,beta;psi)(|D(0+)(gamma,beta;psi)u|(p-2)D(0+)(gamma,beta;psi)u+a(x)|D(0+)(gamma,beta;psi )u|(q-2)D(0+)(gamma,beta;psi )u), where D(T)(gamma,beta;psi )and D-0+(gamma,beta;psi ) are psi-Hilfer fractional derivatives of order 1/p < gamma < 1 and type 0 <= beta <= 1 and a(center dot) is non-negative weight function, and G(center dot) represents Choquard nonlinearities satisfying a certain growth conditions. By employing the mountain pass theorem without the Palais-Smale condition, along with the Hardy-Littlewood-Sobolev inequality, we establish the existence of a weak solution to the aforementioned problem. Our main results are novel and contribute to the literature on problems involving psi-Hilfer derivatives with the p-Laplacian operator. This investigation enhances the scope of understanding in this specific class of problems.
Based on the minimal and simple representations, we introduce two types of Jacobson semisimplicity, m-semisimplicity and s-semisimplicity, of a semirsemirings. S. Every m(s)-semisimple semiring is a subdirect product of m(s)-primitive semirings. It is shown that a commutative s-primitive semiring is either a two element Boolean algebra or a field. Every s-primitive semiring is isomorphic to a 1-fold transitive subsemiring of the semiring of all endomorphisms of a semimodule over a division semiring.
We study a family of inequalities formed by the Fekete-Szeg & ouml; design, making use of the normalized analytic functions in the open unit disk. We investigate the following functional: Psi(z) := z(1-& vartheta;)psi '(z)/ psi(1-& vartheta;)(z) , where & vartheta; > 0 acts on a domain having the starlike with respect to the boundary of the unit disk and symmetric with respect to the real axis. In addition, various presentations of the central result for functions formulated by convolution are investigated. As a special instance of this result, Fekete-Szeg & ouml; issue associated with Special functions (differential operators) is studied. Moreover, by using bounds of the initial Taylor coefficients, we discussed Second Hankel determinant results.
We provide a new sharp result in Bergman spaces of pluriharmonic functions related to the trace operator, extending previously known assertions. Related new estimates for other pluriharmonic spaces in product domains will be also discussed.
In this paper we obtain the boundedness of the higher order commutators of the fractional integral operator of variable order on the grand variable Herz-Morrey spaces.
The concept of hesitant fuzzy sets (HFSs) was first introduced by Torra (V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529-539). In this paper, the concept of HFSs to subalgebra, ideals, and deductive systems of Hilbert algebras is introduced. The relationships between hesitant fuzzy subalgebras (HF subalgebras), hesitant fuzzy ideals (HF ideals), and hesitant fuzzy deductive systems (HF deductive systems) and their level subsets are provided.
This manuscript aims to discuss the existence of solutions for nonlinear boundary value Langevin fractional differential equations involving the generalized Caputo proportional fractional derivative via Kuratowski measure of noncompactness in an arbitrary Banach space. Using the measure of noncompactness approach and M & ouml;nch's fixed point theorem, we demonstrate the existence result. An illustrative example is provided as an application to illustrate our main results.
In this article, it is shown that a map xi : u -> u (not necessarily linear) satisfies xi((A degrees B) . C) = (xi(A) degrees B) . C + (A degrees xi(B)) . C + (A degrees B) . xi(C) holds for all A, B, C is an element of u(if and only if xi is an additive & lowast;-derivation where u a unital & lowast;-algebra over the complex fields C. As applications, we apply our main result to some special classes of unital & lowast;-algebras such as prime & lowast;-algebras, standard operator algebras, factor von Neumann algebras and von Neumann algebras with no central summands of type I-1.
The paper focuses on the existence and multiplicity of weak solutions to nonlinear Kirchhoff-type equations involving psi-Hilfer derivatives with p(& centerdot;)-Laplacian operators and Dirichlet boundary conditions. Through the application of a critical point approach, along with genus theory and variational techniques, we establish the existence and multiplicity results within appropriate fractional psi-Hilfer derivative spaces. Our novel main results contribute to the advancement of the literature on differential equations involving fractional psi-Hilfer generalized curvature phenomena.
. In this paper we construct several classes of non-regular graphs which are co-spectral with respect to all the three matrices, namely, adjacency, Laplacian and normalized Laplacian, and hence we answer a question asked by S. Butler. We make these constructions starting with two pairs (G(1), H-1) and (G(2), H-2) of Acospectral regular graphs, taking their R-graph R(G(i)), R(H-i), i = 1, 2, and finally making some kind of partial joins between R(G(1)) and R(G(2)); and R(H-1) and R(H-2). Moreover, we determine the number of spanning trees and the Kirchhoff index of the newly constructed graphs.
In the open unit disk {& varsigma; is an element of C : |& varsigma;| < 1}, two subclasses of bi-univalent functions related to Horadam polynomials are presented and examined in this paper. For functions belonging to the recently established classes, we obtain the estimates of the first two coefficients. Furthermore, an estimate of the Fekete-Szego problem is provided for functions in these classes. We also provide some observations and draw relevant connections to earlier research.
In this paper, we begin with the definition of the S-resolvent set of a linear relation. Throughout this paper, X will denote a normed linear space over the complex field C. Operator S plays the role of a transition multivalued linear operator from X. It is the main goal of the present note to study the basic spectral properties of T linked to the transition multivalued linear operator S.
Let R be an associative ring with an involution '*'. In this article, we introduce the notions of centrally-extended generalized Jordan *-derivation, centrally extended Jordan left *-centralizer and characterize these mappings in involutive prime rings.
E. Liflyand and F. M & oacute;ricz proved that the Hausdorff operator generated by a function phi is an element of L-1(R) is a linear operator bounded on the real Hardy space H-1(R) by using the classical Fourier transform and the Hilbert transform, they also proved that this operator commutes with Hilbert transform. In this work, we extend these results to the context of q-harmonic analysis associated with the q-Rubin's operator, we introduce the q-Hilbert transform on the real line, we study some of its main properties. Next, we define the q-Hardy spaces H-q(1)(R-q) by means of the q-Hilbert transforms, we finally study the q-Hausdorff operator and we prove the boundedness property and the commuting relation of this operator and q-Hilbert transform in q-Hardy spaces.
