In this paper, we study of a new q-fractional differential operator originated from the Srivastrava-Owa operator of fractional integration with modified q-Opoola derivative operator. The Fekete-Szego H2(1) functional and Second Hankel determinant H2(2) for normalized analytic function belonging to the family of q-starlike and q-convex functions in the open unit disk are investigated.
. To contribute to the development of algebraic semantics, the concept of deductive energetic set in equality algebras is introduced, and several properties are investigated. The conditions under which a subset becomes deductive energetic in an equation algebra are explored, and its characterization is also obtained. The union and intersection of deductive energetic sets are examined. Equality homomorphic (pre) images and direct product of deductive energetic sets are addressed.
The current study addresses a boundary value problem involving integral boundary conditions with Caputo fractional differential equations and employs the boundary value problem (BVP) framework to establish the existence of solutions via Schaefer's fixed point theorem. Additionally, it leverages contraction mapping principles to prove uniqueness and investigates Ulam-Hyers stability of fractional-order BVPs using Gronwall's inequality. As an illustration, three examples are provided to demonstrate the applicability of our main results.
. In 2022, Kim [16] proved a finiteness theorem for a restricted class of universal generalized m-gonal forms; namely, a generalized m-gonal form f with coefficients 1 or 2 is universal if m >= 10 and f represents 1, m- 4 and m- 2. In this paper, we prove a similar finiteness theorem for universal m-gonal forms. If m is even, m >= 10 and an m-gonal form f with coefficients 1 or 2 represents 2m- 1 and 4m- 2, then f is universal, and if m is odd, m >= 7 and f represents either 2m- 1 and 2m- 2 or 2m- 2 and 5m- 4, then f is universal.
In this paper, we firstly present a necessary and sufficient condition for a warped product manifold to be an Einstein-like manifold. By using this condition, we prove that if a warping function is not constant, then the fiber space of an Einstein-like warped product manifold is an Einstein manifold. Moreover we construct new examples of Einstein-like manifold which are not Einstein.
In this paper, we present the induced singular dynamics of the Cartesian product manifold and their homotopy groups. We also analyze the induced limit singular dynamics on the Cartesian product of manifolds and their associated homotopy group. The role played by the dynamical manifold in the wedge sum of manifolds and their homotopy group will be identified. We introduce a certain type of conditional singular dynamical manifold for free group elements and its homotopy group. Theorems concerning these relations are provided. The results we achieved provide new insights into the relationship between singular dynamics and topology by highlighting how a system's history reflects the algebraic structure of its core manifold.
The general sextic functional equation is a generalization of many functional equations such as Jensen, general quadratic, general cubic, general quartic, and general quintic functional equations. In this paper, we investigate the generalized stability of the general sextic functional equation.
In this paper, a new class of analytic function is defined by using an analytic characterization which is influenced by the multiplicative derivative. Multiplicative derivative is defined in a domain which excludes zero, so here the defined subclass did not involve swapping the ordinary derivative with a multiplicative derivative. But we have just used the motivation behind the purpose of such a restrictive calculus, given the circumstances that we have a more versatile calculus of Newton and Euler. Estimates involving the initial coefficients, inclusion and closure properties, which belong to the defined function class are our main results.
. In this paper, we present the semilo cal convergence analysis of the third order Newton-like method in Riemannian manifolds. We study the convergence analysis of our method under Lipschitz continuity condition on the first order covariant derivative of a vector field. Using normal coordinates the order of convergence is derived. Finally, a numerical example is given to show the effectiveness of our results.
IfP(z) =a(n)coproduct(n)(nu=1)(z-z(nu)) is a complex polynomial of degreenhavingall its zeros in|z| <= K, K >= 1 then Aziz (Proc Am Math Soc 89:259-266, 1983)proved that (0.1) max(|z|=1)|P '(z)|>= 2/1 +K-n (n)Sigma K-nu=1/K+|z(nu)|max(|z|=1)|P(z)|. This paper presents a comprehensive analysis that encompasses the refinement of inequality (0.1) while also extending the well-established Turan's inequality. Furthermore, we broaden the scope of our findings by applying them to the polar derivative of a polynomial. Our investigation reveals that the bounds derived from our results exhibit a significantly enhanced level of precision compared to inequality (0.1). To illustrate this, we provide a numerical example to underscore the superior performance of our findings.
The game of SET is a popular card game that involves finding particular visual patterns. In this paper, we introduce a new game rule using a SET card deck, and show that the game is equivalent to finding an affine relation in the affine space AG(4, 3). Furthermore, we observe that similar approaches can be applied to other SET-like card games related to finite affine spaces over other finite fields.
In this paper, we study some basic properties related to separation axioms of the space of closed subsets of a zero-dimensional topological space. Thus we characterize the hyperspace of a zero-dimensional topological space via the notions of normality and partition. Then we establish five equivalent conditions characterizing when the hyperspace of a compact Hausdorff space is zero-dimensional. Furthermore, we give some examples related to our results.
In this paper, we use the features of generalized concave operators to verify the uniqueness of positive solutions and establish the existence of positive solutions for a certain class of fractional differential equations.
In this paper, we introduce and solve the following additive-additive (s,t)(s,t)(s,t)-functional inequality: (1)parallel to 2g (x+y/2)-g(x)-g(y)parallel to+parallel to 2h (x+y/2)+2h (x-y2)-2h(x)parallel to(1/ <=parallel to s(g(x+y)-g(x)-g(y))parallel to+parallel to t(h(x+y)+h(x-y)-2h(x))parallel to where sand t are fixed nonzero complex numbers with divided by s divided by+divided by t divided by<1 . We define a pair of hom-derivation and homomorphism in complex Banach algebras, and using the direct method and the fixed point method, we prove the Hyers-Ulam stability of pairs of hom-derivations and homomorphisms in complex Banach algebras associated with the additive-additive (s,t)(s,t)(s,t)-functional inequality (1) and the following functional inequality: (2)parallel to g(xy)-g(x)h(y)-h(x)g(y)parallel to+parallel to h(xy)-h(x)h(y)parallel to <=phi(x,y)
Given a real parameter alpha and a semigroup S, we consider a functional equation arising from the multiplicative structure of the quartic number field Q((4)root alpha). A recent study by Mouzoun and Zeglami [Bol. Soc. Mat. Mex. 28:73 (2022)] investigated solutions to this equation, yet specific results were found to be incorrect. In this work, we provide a rigorous reexamination of the equation, identify the inaccuracies, and introduce refined conditions that ensure its correct formulation. Our results offer a precise characterization of semigroup homomorphisms associated with the product structure in pure quartic number fields, thereby contributing to the broader study of functional equations in algebraic systems.
By employing the Parallel Axis Theorem for a thin rod, we derive a refined identity that is applicable to an arbitrary sequence. Through the substitution of diverse general sequences within this identity, we establish novel sums of Fibonacci sequences.
In this paper, we investigate the general solution of the following functional equation f(x + 3y) + f(x-3y) = 9(f(x +y) + f(x-y)) + 12f(y)-12f(2y) +4f(3y)-16f(x) and discuss its Hyers-Ulam stability in quasi-Banach spaces.
In the present paper, we introduce the notion of a fuzzy Hilbert C*- module and study the Hyers-Ulam stability of fuzzy Hilbert C*-module homomorphisms and fuzzy Hilbert C*-module derivations in fuzzy Hilbert C*-modules using the fixed point method.
This paper is concerned with a multi-dimensional attraction-repulsion chemotaxis system with nonlinear sensitive functions. A corresponding free boundary problem is derived, and proved the existence of stationary solutions and Hopf bifurcation which are essentially determined by the competition of attraction and repulsion.
It is known that if R is a coherent Prufer ring, which is necessarily a Gaussian ring, then its weak global dimension w. gl. dim(R) must be 0, 1, or oo. In this paper, we investigate the possible values of the weak global dimension for a broader class of Prufer rings that are not necessarily coherent. Our analysis employs four conceptually distinct proofs, each relying on different homological techniques, including localization at the nilradical, finitistic projective dimension, and flatness properties. The results extend the classical framework to a non-coherent setting by incorporating the effective H-D framework, which serves as a surrogate for coherence in controlling homological dimensions. This work aims to deepen the understanding of the weak global dimension in the context of non-coherent Prufer rings and provide a unified perspective on its behavior.
