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In this paper, fractal differential equations are solved numerically. Here, the typical fractal equation is considered as follows: du(t)/dtα = f {t, u(t)}, α > 0, f can be a nonlinear function and the main goal is to get u(t). The continuous and discrete modes of this method have differences, so the subject must be carefully studied. How to solve fractal equations in their discrete form will be another goal of this research and also its generalization to higher dimensions than other aspects of this research. [ABSTRACT FROM AUTHOR]

In this paper, a new version of a higher-order strongly convex function is introduced which is named (ω-σ)-higherorder strongly convex function. Sufficient conditions for the existence of minimum for (ω - σ)-higher order strongly convex function is provided. The vector version of (ω-σ)-higher order strongly convex function is given and by using KKM theory an existence results for a solution of it is proved. Moreover, the compactness of the solution set of the vector version of (ω -σ)-higher order strongly convex function is investigated. The results of this article improve and extend the corresponding results presented in this area. [ABSTRACT FROM AUTHOR]

In the paper, we investigate a class of nondifferentiable semi-infinite multiobjective programming problems such that all functions constituting them are interval-valued. We derive both Fritz John necessary optimality conditions and, under a constraint qualification, Karush-Kuhn-Tucker necessary optimality conditions for (weak) $ LU $-Pareto solutions in the considered nondifferentiable semi-infinite vector interval-valued optimization problem. Under appropriate invexity hypotheses, we also prove sufficient optimality conditions for this semi-infinite interval-valued vector optimization problem. Further, we also use the $ l_{1} $ exact function method for solving the aforesaid nondifferentiable interval-valued multicriteria optimization problem. Then, we analyze the property of exactness of the penalization for the absolute value exact penalty function method under assumption that the functions involved in the considered semi-infinite multiobjective programming problem are locally Lipschitz interval-valued invex functions. The conditions guaranteeing the equivalence of the sets of (weak) $ LU $-Pareto solutions in the original semi-infinite interval-valued multiobjective programming problem and its associated vector penalized optimization problem with the multiple interval-valued $ l_{1} $ exact penalty function are given. [ABSTRACT FROM AUTHOR]

Hyperspectral images have high spectral resolution. But, due to the tradeoff between spectral and spatial resolution and various hardware constraints, imaging a hyperspectral image with high spatial resolution is not practical. Hyperspectral super resolution is a soft approach to solve this challenge. Recently, deep learning based methods such as convolutional neural network (CNN) show great success in this field. But, the contextual details in object boundaries and anomalies present in the scene are not well addressed. To this end, a new CNN based framework is proposed for hyperspectral image super resolution in this work. To improve ability of the convolutional blocks in simultaneous extraction of spectral and spatial characteristics, the weighted Gabor features are concatenated in output of the defined convolutional blocks. To extract more details containing anomalous targets present in the scene, the anomaly scores of pixels are calculated and used for weighting the Gabor features. The experiments on three real hyperspectral images acquired by AVIRIS and ROSIS sensors show superior performance of the proposed framework compared to several state-of-the-art methods based on CNN and residual networks. In addition to common super resolution metrics such as SAM and ERGAS, the efficiency of different methods are evaluated according to the classification accuracy metrics such as overall accuracy and kappa coefficient. The overall classification accuracy is increased from 70.39 to 88.23 in Indian dataset, from 86.07 to 96.20 in Pavia University dataset, and from 95.82 to 99.12 in Pavia center dataset. [ABSTRACT FROM AUTHOR]

Introduction: According to the research conducted in recent years and after the evolution of social networks, the statistics of obesity and the consumption of fast foods and high-calorie foods have increased significantly. Also, food blogging has become much more widespread and popular in the space of social networks, so we are investigating the impact of social networks on people's nutritional habits. Material and Methods: The purpose of this research is to examine the relationship and impact of social networks on people's nutritional habits. For this research, a 20-question questionnaire was answered by 60 college students and the obtained data was analyzed by SPSS 26. Results: The most social media has been used are Instagram, Telegram, and YouTube, and 22% use social media between 3 and 4 hours a day. More than 58% used ready food less than 2 days a week. But 56% of them reported that social media didn’t have a noticeable effect on their informed decision in choosing food. Conclusion: This study showed that the use of social media can be effective in people's lifestyle and food pattern and food intake. [ABSTRACT FROM AUTHOR]

In this paper, by using the notions of approximate pseudo-dissipativity, strong subdifferential and epsilon-subdifferential, we present sufficient optimality conditions for an epsilon-weak local Pareto minimal solution and an epsilon-local Pareto minimal solution of a vector optimization problem, where its objective function and constraint set are in the form of differences of two vector-valued convex maps, respectively. Then, an application of the given result is obtained for vector fractional programming. Also, some comments are given on two recently published papers presented by Guo and Li [Optimality conditions for vector optimization problems with difference of convex maps. J Optim Theory Appl. 2014;162:821–844] and Gadhi and Metrane [Sufficient optimality condition for vector optimization problems under D.C. J Glob Optim. 2004;28:55–66]. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result. [ABSTRACT FROM AUTHOR]

The objective of this paper is to determine a modified SP-iteration process for multi-valued mappings and to establish the convergence theorems for sequences generated by modified SP-iteration processes involving multi-valued Suzuki mappings converging to endpoints in uniformly convex hyperbolic spaces. The numerical example for supporting our main result is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we establish two versions of the existence theorems of solutions set of generalized vector variational-like inequalities in fuzzy environment by using two different notions; the first one by using affineness and the second by using the notion of vector O-diagonally convexity. Moreover, an example is established in order to illustrate the main problem. The results of this paper can be viewed as a significant improvement and refinement of several other previously existing known results. [ABSTRACT FROM AUTHOR]

In this paper, an iterative process for a hybrid pair of a finite family of generalized I-asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive multi-valued mappings is established. Moreover, the weak convergence theorems and strong convergence theorems of the proposed iterative process in Banach spaces are proven. The examples are established for supporting our main results. The obtained results can be viewed as an improvement and extension of the several results in the literature. [ABSTRACT FROM AUTHOR]