For the well developed notion of approximate Birkhoff-James orthogonality, in a real or complex normed linear space, we formulate a new characterization. It can be derived from other, already known, characterizations ...
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For the well developed notion of approximate Birkhoff-James orthogonality, in a real or complex normed linear space, we formulate a new characterization. It can be derived from other, already known, characterizations as well as obtained in a more elementary and direct way, on the basis of some simple inequalities for real convex functions.
This article explores the integration of HermiteHadamard Type Inequalities and convex functions within the domain of signal processing, elucidating their theoretical underpinnings and practical implications. Beginning...
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This article explores the integration of HermiteHadamard Type Inequalities and convex functions within the domain of signal processing, elucidating their theoretical underpinnings and practical implications. Beginning with a comprehensive background, we focus on the historical context and foundational concepts that underlie these mathematical constructs. Our discussion progresses to articulate the problem formulation, delineating the specific challenges and objectives addressed in the study. The theoretical framework elucidates the HermiteHadamard Type Inequalities, highlighting their mathematical formulations, properties, and fundamental proofs. Concurrently, the discourse unfolds the theory and properties of convex functions, elucidating their significance and applications within signal processing paradigms. With a focus on applications, we illustrate the utility of Hermite-Hadamard Type Inequalities and convex functions in signal processing tasks. Through empirical studies and case examples, we demonstrate their efficacy in signal denoising, compression, and feature extraction, showcasing tangible results and comparative analyses. We discuss the challenges and limitations inherent in the application of these mathematical constructs in real-world scenarios, thereby paving the way for future research directions and advancements. Finally, we conclude by summarizing the key insights gleaned from our exploration and underscore the profound implications of Hermite-Hadamard Type Inequalities and convex functions in shaping the landscape of contemporary signal processing methodologies.
This article finds q- and h-integral inequalities in implicit form for generalized convex functions. We apply the definition of q - h-integrals to establish some new unified inequalities for a class of (alpha, & h...
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This article finds q- and h-integral inequalities in implicit form for generalized convex functions. We apply the definition of q - h-integrals to establish some new unified inequalities for a class of (alpha, & hbar;- m)-convex functions. Refinements of these inequalities are given by applying a class of strongly (alpha, & hbar;- m)-convex functions. Several q-integral inequalities for various kinds of convex and strongly convex functions are deduced under specific conditions.
The main object of this article is to present the sharp bounds of the third -order Hankel determinant for functions in a subclass of normalized analytic functions in the open unit disk D, which are the inverses of the...
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The main object of this article is to present the sharp bounds of the third -order Hankel determinant for functions in a subclass of normalized analytic functions in the open unit disk D, which are the inverses of the class of Ozaki type close to convex functions. Several earlier developments, which are related to our main results, are also described. (c) 2023 Elsevier Masson SAS. All rights reserved.
Let K-u denote the class of all analytic functions f in the unit disk D := {z is an element of C : |z| < 1}, normalised by f (0) = f'(0) - 1 = 0 and satisfying |zf'(z)/g(z) - 1| < 1 in D for some starlik...
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Let K-u denote the class of all analytic functions f in the unit disk D := {z is an element of C : |z| < 1}, normalised by f (0) = f'(0) - 1 = 0 and satisfying |zf'(z)/g(z) - 1| < 1 in D for some starlike function g. Allu, Sokol and Thomas ['On a close-to-convex analogue of certain starlike functions', Bull. Aust. Math. Soc. 108 (2020), 268-281] obtained a partial solution for the Fekete-Szeg(sic) problem and initial coefficient estimates for functions in K-u, and posed a conjecture in this regard. We prove this conjecture regarding the sharp estimates of coefficients and solve the Fekete-Szeg(sic) problem completely for functions in the class K-u.
Let S denote the class of analytic and univalent functions in the unit disk D = {z is an element of C : |z| < 1} of the form f (z) = z +Sigma (infinity) (n=2) a(n)z(n). For f is an element of S, the logarithmic coe...
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Let S denote the class of analytic and univalent functions in the unit disk D = {z is an element of C : |z| < 1} of the form f (z) = z +Sigma (infinity) (n=2) a(n)z(n). For f is an element of S, the logarithmic coefficients defined by log (f (z)/z) = 2 Sigma (infinity) (n=1) gamma(n)z(n), z is an element of D. In 1971, Milin [12] proposed a system of inequalities for the logarithmic coefficients of S. This is known as the Milin conjecture and implies the Robertson conjecture which implies the Bieberbach conjecture for the class S. Recently, the other interesting inequalities involving logarithmic coefficients for functions in S and some of its subfamilies have been studied by Roth [24], and Ponnusamy et al. [17]. In this article, we estimate the logarithmic coefficient inequalities for certain subfamilies of Ma-Minda family defined by a subordination relation. It is important to note that the inequalities presented in this study would generalize some of the earlier work. (c) 2024 Elsevier Masson SAS. All rights reserved.
This paper explores the class CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...
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This paper explores the class CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{C}_{G}$\end{document}, consisting of functions g that satisfy a specific subordination relationship with Gregory coefficients in the open unit disk E. By applying certain conditions to related coefficient functionals, we establish sharp estimates for the first five coefficients of these functions. Additionally, we derive bounds for the second and third Hankel determinants of functions in CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{C}_{G}$\end{document}, providing further insight into the class's properties. Our study also investigates the logarithmic coefficients of log(g(t)t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\log \left ( \frac{g(t)}{t}\right ) $\end{document} and the inverse coefficients of the inverse functions (g-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(g<^>{-1})$\end{document} within the same class.
Let f be analytic in the unit disk D = {z is an element of C : |z| < 1 }. We obtain bounds of |H (2 , 3) |, where H (2 ,3) = a( 3) a( 5 )- a( 4) (2) for two classes S( & lowast;)and k consisting of starlike and...
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Let f be analytic in the unit disk D = {z is an element of C : |z| < 1 }. We obtain bounds of |H (2 , 3) |, where H (2 ,3) = a( 3) a( 5 )- a( 4) (2) for two classes S( & lowast;)and k consisting of starlike and convex univalent functions, respectively. Additionally, we derive the sharp upper bounds of H- 2 ,H-3 in case of real coefficients. (c) 2024 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this letter, we give an exact characterization of the set of possible minimizers of...
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Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this letter, we give an exact characterization of the set of possible minimizers of the sum. Our results cover several types of assumptions on the summands, such as smoothness or strong convexity. Our main tool is the use of necessary and sufficient conditions for interpolating the considered function classes, which leads to shorter and more direct proofs in comparison with previous work. We also address the setting where each summand minimizer is assumed to lie in a unit ball, and prove a tight bound on the norm of any minimizer of the sum.
The electrical capacitance tomography technology has potential benefits for the process industry by providing visualization of material distributions. One of the main technical gaps and impediments that must be overco...
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The electrical capacitance tomography technology has potential benefits for the process industry by providing visualization of material distributions. One of the main technical gaps and impediments that must be overcome is the low-quality tomogram. To address this problem, this study introduces the data-guided prior and combines it with the electrical measurement mechanism and the sparsity prior to produce a new difference of convex functions programming problem that turns the image reconstruction problem into an optimization problem. The data-guided prior is learned from a provided dataset and captures the details of imaging targets since it is a specific image. A new numerical scheme that allows a complex optimization problem to be split into a few less difficult subproblems is developed to solve the challenging difference of convex functions programming problem. A new dimensionality reduction method is developed and combined with the relevance vector machine to generate a new learning engine for the forecast of the data-guided prior. The new imaging method fuses multisource information and unifies data-guided and measurement physics modeling paradigms. Performance evaluation results have validated that the new method successfully works on a series of test tasks with higher reconstruction quality and lower noise sensitivity than the popular imaging methods.
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