Results 171 to 180 of about 183,031 (208)
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Remarks on strongly convex functions
Aequationes mathematicae, 2010Let \(I\subseteq \mathbb{R}\) be an interval and \(c\) be a positive number. A function \(f:I\rightarrow \mathbb{R}\) is called strongly convex with modulus \( c\) if \[ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-ct(1-t)(x-y)^{2}, \] for all \(x,y\in I\) and \(t\in [0,1]\).
Merentes, Nelson, Nikodem, Kazimierz
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On strongly convex sets and strongly convex functions
Journal of Mathematical Sciences, 2000The basic notions of this paper are generating set and \(M\)-strongly convex set, which have grown from the axiomatic approach to the notion of convexity. A convex closed set \(M\) of a Banach space \(E\) is called a generating set if for any nonempty set \(A\) of the form \(A=\bigcap_{x\in X}(M+x)\) one can find a convex closed set \(B\subset E\) such
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Higher Order Strongly m-convex Functions
2021Some new concepts of the m-convex functions, where m ∈ (0, 1] are introduced and studied. Basic properties of m-convex functions are discussed. New modified Regula Falsi methods are suggested for solving nonlinear equations. Characterizations of the higher order strongly m-convex functions are investigated under suitable conditions.
Muhammad Aslam Noor, Khalida Inayat Noor
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Relative Strongly Exponentially Convex Functions
2020In this paper, we define and consider some new concepts of the strongly exponentially convex functions involving an arbitrary negative bifunction. Some properties of these strongly exponentially convex functions are investigated under suitable conditions.
Muhammad Aslam Noor +2 more
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Strongly convex functions of higher order
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ger, Roman, Nikodem, Kazimierz
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INVARIANCE OF THE COEFFICIENTS OF STRONGLY CONVEX FUNCTIONS
Bulletin of the Australian Mathematical Society, 2016Let the function $f$ be analytic in $\mathbb{D}=\{z:|z|<1\}$ and given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$. For $0<\unicode[STIX]{x1D6FD}\leq 1$, denote by ${\mathcal{C}}(\unicode[STIX]{x1D6FD})$ the class of strongly convex functions.
Thomas, D. K., Verma, Sarika
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Functions Generating Strongly Schur-Convex Sums
2012The notion of strongly Schur-convex functions is introduced and functions generating strongly Schur-convex sums are investigated. The results presented are counterparts of the classical Hardy–Littlewood–Polya majorization theorem and the theorem of Ng characterizing functions generating Schur-convex sums.
Kazimierz Nikodem +2 more
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On the properties of strongly hd convex functions
Annals of the University of Craiova Mathematics and Computer Science SeriesWe study some optimization properties of $h_d$ strongly convex functions. More precisely, we discuss the characterization properties/inequalities (existence and uniqueness) of minima of $h_d$ strongly convex functions. Moreover, connections with polynomial norms are also presented.
Lăchescu Geanina-Maria +1 more
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On the Approximation by $\phi$-Strongly Convex Functions
Real Analysis ExchangeThe work provides a sandwich type statement for approximating real functions by \(\Phi\)-strongly modulus \(c\) convex functions and some related results, in particular a counterexample showing that similar results do not exist for other types of functions.
Bahos-Orjuela, Cesar M. +2 more
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