In this article, we introduce the notions of deferred Euler statistical convergence with respect to power series as well as g-deferred Euler statistical convergence in the sense of power series method for double sequences of real numbers. Furthermore, we establish applications of these convergences in the form of a Korovkin-type approximation theorem. Finally, we determine the rate of convergence.
In this paper, we show that every rough Wijsman convergent nested sequence of sets is rough Hausdorff convergent to the same set. In addition, we characterize the rough Hausdorff limit and rough Wijsman limit of a sequence by using the unions and intersections of the r-enlargement terms of this sequence.
In this paper, the helices and polynomial curves of constant breadth are investigated using the Frenet-like curve frame in Euclidean 3-space. It is shown that in some exceptional cases, the polynomial space curves of constant breadth are helices. Moreover, the differential equations characterizing the polynomial space curves of constant breadth in Euclidean 3-space are presented.
In this paper, we investigate the tricolorability of alternating potholder diagrams APn, a class of knot diagrams constructed over the potholder curve Pn. Tricolorability is a combinatorial property used to distinguish different knot types by assigning three colors to the strands of a knot diagram under specific rules. We identify which alternating potholder diagrams are tricolorable.
In this article, using the q-calculus, the resolvent of the qSturm-Lioville operator under impulsive boundary conditions is discussed. In this context, the historical development of the subject is discussed in the introduction. In the Preliminaries section, the basic concepts of qcalculus are given, i.e., q-derivative and q-integral definitions are given, and a Hilbert space for impulsive q-Sturm-Liouville problems is defined. In the main results section, Green's function corresponding to the impulsive q-Sturm-Liouville problem is established. With the help of Green's function, the resolvent operator for the impulsive q-Sturm-Liouville problem is defined. The compactness of the resolvent operator corresponding to the impulsive q-Sturm-Liouville problem is obtained by showing that this function is a Hilbert-Schmidth kernel. The spectral function corresponding to the impulsive q-Sturm-Liouville operator is generated. Using the spectral function, the integral representation of the resolvent operator of the impulsive q-Sturm-Liouville operator in the singular case is obtained.
In this paper, a novel class of univalent functions is defined on the open unit disc U, closely related to the class of starlike functions defined with respect to a boundary point. To demonstrate the non-emptiness of the class, illustrative examples are constructed. Furthermore, a Herglotz representation theorem for the new class is formulated and proved.
In this study, the components of the Darboux frame associated with a Legendre curve lying on a surface in the BCV-Sasakian space are derived for the first time. The geometric invariants of the curve, namely its normal curvature, geodesic curvature, and geodesic torsion, are explicitly computed. A canal surface is then constructed around the Darboux-framed BCV-Legendre curve, leading to the formulation of Darboux-framed BCV-Legendre tubes. The intrinsic and extrinsic geometry of these tubular surfaces is investigated by calculating their Gaussian and mean curvatures. Moreover, the relationships between the parameter curves and geodesics, asymptotic curves, and curvature lines on the Darboux-framed BCV-Legendre tubes are analyzed in detail. All of these results are obtained for the first time in the context of BCV-Sasakian geometry, thus providing an original and significant contribution to the differential geometry of contact manifolds.
The growth and distortion theorems provide bounds on how much a univalent function can stretch or distort distances and shapes in the complex plane. It is closely associated with the theory of univalent functions. The radius estimates in univalent function theory offer valuable insights into the behavior of analytic and univalent functions, helping to determine the domains within which these functions maintain various properties such as starlikeness, convexity, close-to-convexity, etc. The main aim of this manuscript is to investigate the growth and distortion theorem, as well as various types of radius estimates, for a certain class of quotient functions with a fixed second coefficient defined on the open unit disk.
In this paper, we study the relation between biflatness and left character amenability of Banach algebras. Moreover, we prove that if A is a phi-biflat Banach algebra with a closed ideal I such that AI + IA = I, then the quotient algebra A/I is phi e-biflat. These results correct certain conclusions from [5], and we provide counterexamples that highlight the shortcomings of some of the claims made in that work.
In this paper, we examine the Finsler space Fn with Randers 3-transformed homogeneous metric given by cY + 3 f (cY, 3), where cY = ,./aij(x)yiyj represents the Riemannian metric, 3 = bi(x)yi denotes a one-form metric, and f(cY, 3) is a zero-degree homogeneous function of the variables cY and 3. If bi(x) is the gradient of a scalar function b(x), then the hypersurface F(n-1) c in the Finsler space is defined by the equation b(x) = c where c is a constant. Based on this framework, we derive the necessary and sufficient conditions for the hypersurface F(n-1) c to be a hyperplane of the first or second kind. Additionally, we demonstrate that F (n-1) c can never be a hyperplane of the third kind.
In this paper, for double sequences, we introduce the notions of Ces & agrave;ro convergence, statistical convergence and statistically Cauchy sequence in 2-metric space. Also, we investigate some inclusion relations between these concepts in 2-metric space.
This paper introduces new criteria for determining starlike functions by extending classical results in several directions. We develop starlikeness conditions involving higher-order derivatives, propose operator-based approaches, and explore the extension of these criteria to alternative domains such as annuli and punctured disks. These generalizations reveal deep connections between geometric properties and analytic structures, offering fresh perspectives in geometric function theory. Additionally, we establish new results for subclasses of analytic functions and discuss their implications for univalence and convexity.
In this paper we provide explicit computations of filtered wrapped Floer homology of real Lagrangians in Milnor fibers of homogeneous polynomials. As an application, we discuss the volume growth of fibered twists on those Milnor fibers.
This paper introduces a new subclass of uniformly convex functions with negative coefficients defined by the Miller Ross-type Poisson distribution series. We obtain the coefficient bounds, extreme points closure theorems, and radii of starlikeness and convexity for functions belonging to the class. Furthermore, we discussed partial sums and neighborhood results for this class.
In this work, amply cofinitely weak essential supplemented (briefly, amply cwe-supplemented) modules are defined and some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of an amply cwe-supplemented module are amply cwe-supplemented. It is also proved that every ii-projective and cwe-supplemented module is amply cwe-supplemented. Let Lambda be any index set and {M lambda}Lambda be a family of projective R-modules. If M lambda is cwesupplemented for every lambda is an element of Lambda, then circle plus M lambda is amply cwe-supplemented. lambda is an element of Lambda Let M be a projective R-module. If M is cwe-supplemented, then every M-generated R-module is amply cwe-supplemented. Let R be any ring. Then every R-module is cwe-supplemented if and only if every R-module is amply cwe-supplemented.
We characterize pluriharmonic symbols for zero sums of finitely many products of two weighted Bergman dual Toeplitz operators on the tube domain. Our results demonstrate that several known results on the unit ball or polydisk continue to hold for all tube domains.
In this work, we investigate the intriguing geometry of ruled surfaces in three-dimensional Euclidean space that are produced by Smarandache curves with a modified orthogonal frame. The TN-Smarandache, TB-Smarandache, and NB-Smarandache surfaces are three different kinds of ruled surfaces by using the modified orthogonal frame of an arbitrary regular curve. We formally analyze these surfaces to acquire theorems providing necessary and sufficient requirements for these surfaces to have minimality and developability, as well as nonexistence theorems for specific situations. This approach reveals unique geometric insights into the properties and behavior of these specific ruled surfaces. In order to visualize the structural details of each surface type, we provide an example and related images to demonstrate some results.
In this work, essential N-projective (briefly, e-N-projective) modules are defined for an R-module N and some properties of these modules are investigated. It is proved that any direct sum of essential N-projective modules is essential N-projective. Let M be an R-module and N (sic) M. If M/N is essential M-projective, then N = M. Let M be an R-module and 0 -> K (f) -> N (g) -> T -> 0 be any short exact sequence with f (K) (sic) N. If M is essential N-projective, then M is essential K and T-projective. Let M be an R-module. Then every R-module is essential M-projective if and only if every R-module is M-projective. Let M be an R-module. If M is essential M-projective, then M is called a self essential projective module. Let M be a self essential projective module and K be a fully invariant submodule of M. Then M/K is self essential projective.
When the beta-expansions of rational numbers are periodic mechanical words, the periodicity makes beta a zero of a polynomial with integer coefficients. Further, the dynamics of mechanical words enables us to estimate the locations of the other zeros. As a consequence, we specify a class of irreducible polynomials over Q-a scene where dynamics plays a pivotal role in demonstrating a purely algebraic property.
In this work, we define a new class t-SSP of starlike functions with respect to t-symmetric points. Based on this definition, we will introduce two new subclasses, t-SSP(gamma, beta) and t-SSP(A, B). Furthermore, for functions in each of the subclasses introduced here, we obtain some majorization problem, corollaries and given by earlier workers on the subject are pointed out.
