Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to $L_p$ spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in $L_p$ spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas.

Varaždin County is rich in mineral resources, attracting considerable investor interest in opening new exploration areas and expanding existing exploitation fields. Since the economic value of mineral resources changes with market conditions, continuous professional assessment is required. Although the proposed methodological framework is broadly applicable to mineral resource management, this case study focuses on the exploitation of construction sand and gravel deposits in Varaždin County. In this way, it addresses the sustainability challenges characteristic of quarry operations rather than large-scale mining projects. The objective of this study was to develop and test a new method for quantifying sustainability indicators in the mineral resource management (spatial, resource-related, environmental, economic, and social sustainability—I_PREGS) and for calculating an aggregated composite index (AK_I) using a pilot project for construction sand and gravel. The research establishes a cause–effect relationship between quantified indicators (I_PREGS) and the newly established aggregated composite index (AK_I). Methodologically, the study applied multivariate analysis to questionnaire data, enabling the selection, weighting, and aggregation of indicators and the design of a conceptual framework for AK_I calculation. The resulting methodology provides an instrument for monitoring and improving sustainable mineral resource management, supporting the objectives of the circular economy. The findings highlight the potential of the AK_I to reduce systemic inefficiencies, guide policy development, and offer a transparent mechanism for assessing both implementation and effectiveness. This significantly improves the current state and strengthens the basis for evidence-based economic policy-making. The case study in Varaždin County further demonstrated that the AK_I not only reproduces administrative decisions with high consistency but also clarifies how applicants should proceed in cases of partial acceptance and how policymakers can interpret conflicting outcomes across different index variants.

In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of $n$-th derivatives are $(\alpha ,m)$-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. As a special case, the generalization of the remainder term of the midpoint and trapezoidal quadrature formulas are obtained.

Urban recreational lakes require systematic microbiological monitoring to ensure public health protection and agreement with bathing-water regulations. This study investigates the spatial variability in fecal indicator bacteria (Escherichia coli and intestinal enterococci) at two major urban bathing sites in Zagreb, Croatia (Lake Bundek and Lake Jarun), using a four-year monitoring dataset (2016–2019) collected at 19 fixed sampling locations. E. coli was quantified using a miniaturized most probable number (MPN) method, while intestinal enterococci were determined by membrane filtration, following ISO standards. Microbiological concentrations were log₁₀-transformed and analyzed using one-way analysis of variance (ANOVA) to test for statistically significant differences among sampling locations within each lake. Variability in microbiological data was characterized using box-and-whisker plots, which appropriately represent dispersion and skewness typical of MPN- and CFU-based measurements. The results indicate predominantly homogeneous spatial distributions of both indicators, particularly at Lake Jarun, where no statistically significant differences among sampling locations were observed. In contrast, a statistically significant spatial difference in E. coli concentrations was detected at Lake Bundek, likely reflecting site-specific characteristics such as smaller lake size and more limited water exchange.