JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY

Publisher:: —
ISSN:: 1976-8605
Category:: MATHEMATICS, APPLIED
Impact factor:: 0.7

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

2026-03-29

Muntazeer Ansari, Lakshmi Narayan Mishra

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

2026-03-29

Young Joo SEO

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.

On Some Turan-type Inequalities for Derivative of a Polynomial

2026-03-29

Ishfaq Nazir, Irfan Ahmad Wani, Firdose Ahmad

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.