New bounds for soft margin estimator via concavity of Gaussian weighting function

Ullah, Hidayat; Khan, Muhammad Adil; Pečarić, Josip

doi:10.1186/s13662-020-03103-z

Cited by 13 publications

(9 citation statements)

References 24 publications

(17 reference statements)

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“…In the diverse elds of science, convex functions are of the greatest importance due to their dominant manners and wealthy structure [1][2][3]. In recent years, the abundant applicability of convex functions has been observed in engineering [4], di erential equations [5], epidemiology [6], information theory [7], statistics [8], optimization [9], and many others. Moreover, convex functions have some unique properties and, due to such properties, it became a focus point for researchers [10,11].…”

Section: Introductionmentioning

confidence: 99%

Estimations of the Slater Gap via Convexity and Its Applications in Information Theory

Khan

Ullah

Saeed

et al. 2022

Mathematical Problems in Engineering

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Convexity has played a prodigious role in various areas of science through its properties and behavior. Convexity has booked record developments in the field of mathematical inequalities in the recent few years. The Slater inequality is one of the inequalities which has been acquired with the help of convexity. In this note, we obtain some estimations for the Slater gap while dealing with the notion of convexity in an extensive manner. We acquire the deliberated estimations by utilizing the definition of convex function, Jensen’s inequality for concave functions, and triangular, power mean, and Hölder inequalities. We discuss several consequences of the main results in terms of inequalities for the power means. Moreover, by utilizing the main results, we give estimations for the Csiszár and Kullback–Leibler divergences, Shannon entropy, and the Bhattacharyya coefficient. Furthermore, we present some estimations for the Zipf–Mandelbrot entropy as additional applications of the acquired results. The perception and approaches adopted in this note may pretend more research in this direction.

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Section: Introductionmentioning

confidence: 99%

Estimations of the Slater Gap via Convexity and Its Applications in Information Theory

Khan

Ullah

Saeed

et al. 2022

Mathematical Problems in Engineering

Self Cite

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“…Suppose that T L hi represents the results of the high-resolution animated video image after sparse coding, the H(•) function is regarded as a unit step function, the results of sparse coding are quantized, the histogram coding is completed, and the deep detail features of the high-resolution animated video image are extracted, that is, [27,28]…”

Section: Image Reconstruction Methods Of Multiframe Animationmentioning

confidence: 99%

Animation Design Based on 3D Visual Communication Technology

Shan

Wang

2022

Scientific Programming

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The depth synthesis of image texture is neglected in the current image visual communication technology, which leads to the poor visual effect. Therefore, the design method of film and TV animation based on 3D visual communication technology is proposed. Collect film and television animation videos through 3D visual communication content production, server processing, and client processing. Through stitching, projection mapping, and animation video image frame texture synthesis, 3D vision conveys animation video image projection. In order to ensure the continuous variation of scaling factors between adjacent triangles of animation and video images, the scaling factor field is constructed. Deep learning is used to extract the deep features and to reconstruct the multiframe animated and animated video images based on visual communication. Based on this, the frame feature of video image under gray projection is identified and extracted, and the animation design based on 3D visual communication technology is completed. Experimental results show that the proposed method can enhance the visual transmission of animation video images significantly and can achieve high-precision reconstruction of video images in a short time.

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“…Recently in literature, 15 the authors used Green functions and 4‐convex functions and derived improvements of Jensen's inequality and also presented several applications. Jensen's inequality for Sugeno integral is given in Abbaszadeh et al 16 For more interesting results related to celebrated Jensen's inequality, we recommend previous works 17–24 . In this point of view, the authors presented a bound for its difference in Khan et al 25 as follows:…”

Section: Introductionmentioning

confidence: 99%

A new approach for the derivation of bounds for the Jensen difference

Khan

Erden

et al. 2021

Math Methods in App Sciences

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There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi‐arithmetic, and power means. Finally, we give some applications in information theory.

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New bounds for soft margin estimator via concavity of Gaussian weighting function

Cited by 13 publications

References 24 publications

Estimations of the Slater Gap via Convexity and Its Applications in Information Theory

Estimations of the Slater Gap via Convexity and Its Applications in Information Theory

Animation Design Based on 3D Visual Communication Technology

A new approach for the derivation of bounds for the Jensen difference

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