International Journal of Open Problems in Computer Science and Mathematics

Application of Kharrat-Toma Iterative Method for Solving Fractional Differential Equations

Ahmed Anber — 2025-11-09

In this paper, we apply the Kharrat-Toma Iterative Method (KTIM) for solving some fractional di¤erential equations with caputo derivative. This method is combined from the Iterative method and Kharrat-Toma Transform. The obtained results are compared with the exact solutions and some examples are given to show the accuracy of the method.

On Certain Integral Operator Inequalities in Normed Spaces

Anthony Wafula — 2025-11-10

A lot of researches have been carried out on inner product type integral transformers (IPTIT) with regard to various aspects including spectra, numerical ranges and operator inequalities. Consider $M$ and $N$ to be weakly $\mu$-measurable operator valued (OV) functions such that $M,N:\Omega\rightarrow B(X)$ for any $Q\in \mathcal{B}(H).$ If $M$ and $N$ are integrable with respect to Gel'fand axiom, then we obtain a linear transformation arising from the inner product space as $Q\mapsto \int_{\Omega}M_{t}QN_{t}\partial(t).$ There exists an open problem regarding IPTIT while studying inequalities for IPTIT with spectra limited to the unit disc in complex domains. It has been pointed out that the inequalities, and in particular Cauchy-Schwarz (CS) and Cauchy-Buniakowski-Schwarz (CBS) inequalities, can only be attained for these IPTIT if only one of the operator $M$ or $N$ is normal. Therefore, in this note we solve this problem by obtaining CBS-inequalities for IPTIT in Banach spaces.

Tracing the Origins and Generalizations of a Class of Moving Point Inequalities

Shanpeng zeng — 2025-11-30

This research begins with the Guggenheimer inequality and systematically reviews its developmental progress, which has generally undergone stages of degree generalization, form strengthening, and weighted generalization. Following this, inequalities structurally similar to the Guggenheimer inequality have continuously emerged. The Hungarian Mathematical Competition of 2015–2016 presented an inequality with a similar structure. A higher-degree generalization of this inequality leads to a more general form of moving point inequality. By combining the structure of the strengthened generalization of the Guggenheimer inequality, five conjectures with similar structures are proposed.

On geometrical Aspects of Various Operators and their Orthogonality in Complex Normed Spaces

Benard Okelo — 2025-11-30

Studies involving orthogonality of operators is an area with various applications with regard to the ever dynamic and emerging technological research outputs. In normed spaces (NS) there are different types of orthogonality. Useful results have come up where operators possessing given conditions are chosen for Range-Kernel orthogonality to be established. However, most of the results have been focussing on one type of orthogonality called the Birkhoff-James which we have given more results on. In this paper we give results on various notions of orthogonality by considering certain geometrical aspects in NS.