Korean Journal of Mathematics

Coefficient problems on q-fractional integral operator defined by modified q-opoola differential operator

2024-07-15T17:36:38+09:00

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 $H_{2}(1)$ functional and Second Hankel determinant $H_{2}(2)$ for normalized analytic function belonging to the family of $q$-starlike and $q$-convex functions in the open unit disk are investigated.

On Some Turan-type Inequalities for Derivative of a Polynomial

2024-09-10T22:23:50+09:00

If $P(z) = a_{n}\prod_{\nu=1}^{n}

(z - z _{\nu} )$ is a complex polynomial of degree $n$ having all its zeros

in $|z| \leq K,$ $K \geq 1$ then Aziz (Proc Am Math Soc 89:259-266, 1983) proved that

\begin{align*}

\max_{|z|=1} |P'(z)| \geq \frac{2}{1+K^{n}} \sum_{\nu=1}^{n}\frac{K}{K+|z_{\nu}|} \max_{|z|=1} |P(z)|. \tag{0.1}

\end{align*}

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.

Analysis of Ulam-Hyers stability and the existence of solutions in nonlinear Caputo fractional differential equations involving integral boundary conditions

2025-12-06T15:30:54+09:00

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 Gr\"{o}nwall's inequality. As an illustration, three examples are provided to demonstrate the applicability of our main results.

Deductive energetic sets in equality algebras

2025-09-16T20:49:42+09:00

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.

Generalized stability of a general sextic functional equation

2025-12-06T15:45:50+09:00

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.

Estimates for a subclass of starlike functions involving a exponential function

2026-01-14T00:07:00+09:00

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.

Singular dynamics on manifolds: A Cartesian product approach to homotopy group

2026-01-19T16:32:05+09:00

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.

Einstein-like warped product manifolds which are not Einstein

2025-11-24T11:26:17+09:00

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.

Semilocal Convergence Analysis of the third order Newton-like method in Riemannian manifolds

2026-02-21T10:42:58+09:00

In this paper, we present the semilocal 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.

A Finiteness Theorem for Universal $m$-Gonal Forms with coefficients $1$ or $2$

2026-02-20T23:08:16+09:00

In 2022, Kim \cite{k} 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 $m\ge10$ 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, $m\ge10$ 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, $m\ge7$ and $f$ represents either $2m-1$ and $2m-2$ or $2m-2$ and $5m-4$, then $f$ is universal.