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Pavlovsky, Vladislav A., and Igor L. Vasiliev. "On properties of h-differentiable functions." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 5, 2021): 29–37. http://dx.doi.org/10.33581/2520-6508-2021-2-29-37.
Research in the theory of functions of an h-complex variable is of interest in connection with existing applications in non-Euclidean geometry, theoretical mechanics, etc. This article is devoted to the study of the properties of h-differentiable functions. Criteria for h-differentiability and h-holomorphy are found, formulated and proved a theorem on finite increments for an h-holomorphic function. Sufficient conditions for h-analyticity are given, formulated and proved a uniqueness theorem for h-analytic functions.
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Gaydu, Michaël. "An iterative method for solving $$H$$ H -differentiable inclusions." Rendiconti del Circolo Matematico di Palermo (1952 -) 63, no. 3 (June 27, 2014): 389–97. http://dx.doi.org/10.1007/s12215-014-0161-y.
Romanov, V. A. "Asymptotics of H-continuous and H-differentiable measures in Hilbert space." Mathematical Notes of the Academy of Sciences of the USSR 37, no. 1 (January 1985): 49–53. http://dx.doi.org/10.1007/bf01652514.
Buczolich, Zoltán. "Functions with finite intersections with analytic functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 3-4 (1989): 271–75. http://dx.doi.org/10.1017/s0308210500018746.
SynopsisWe prove that for every dense Gδ set H, there exists a continuous function f, such that f intersects every analytic function in finitely many points and f is infinitely differentiable exactly at the points of H. This answers a problem of S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss. They proved a result which implies that every continuous function with finite intersections with analytic functions is infinitely differentiable at the points of a dense Gδ set.
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Latif, Muhammad Amer, Sever Silvestru Dragomir, and Ebrahim Momoniat. "Some weighted integral inequalities for differentiable h-preinvex functions." Georgian Mathematical Journal 25, no. 3 (September 1, 2018): 441–50. http://dx.doi.org/10.1515/gmj-2016-0081.
AbstractIn this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.
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Hernández-Verón, Miguel A., Sonia Yadav, Ángel Alberto Magreñán, Eulalia Martínez, and Sukhjit Singh. "An Algorithm Derivative-Free to Improve the Steffensen-Type Methods." Symmetry 14, no. 1 (December 21, 2021): 4. http://dx.doi.org/10.3390/sym14010004.
Solving equations of the form H(x)=0 is one of the most faced problem in mathematics and in other science fields such as chemistry or physics. This kind of equations cannot be solved without the use of iterative methods. The Steffensen-type methods, defined using divided differences are derivative free, are usually considered to solve these problems when H is a non-differentiable operator due to its accuracy and efficiency. However, in general, the accessibility of these iterative methods is small. The main interest of this paper is to improve the accessibility of Steffensen-type methods, this is the set of starting points that converge to the roots applying those methods. So, by means of using a predictor–corrector iterative process we can improve this accessibility. For this, we use a predictor iterative process, using symmetric divided differences, with good accessibility and then, as corrector method, we consider the Center-Steffensen method with quadratic convergence. In addition, the dynamical studies presented show, in an experimental way, that this iterative process also improves the region of accessibility of Steffensen-type methods. Moreover, we analyze the semilocal convergence of the predictor–corrector iterative process proposed in two cases: when H is differentiable and H is non-differentiable. Summing up, we present an effective alternative for Newton’s method to non-differentiable operators, where this method cannot be applied. The theoretical results are illustrated with numerical experiments.
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Walther, Hans-Otto. "Delay Differential Equations with Differentiable Solution Operators on Open Domains in C((-∞, 0], Rn) and Processes for Volterra Integro-Differential Equations." Contemporary Mathematics. Fundamental Directions 67, no. 3 (December 15, 2021): 483–506. http://dx.doi.org/10.22363/2413-3639-2021-67-3-483-506.
For autonomous delay differential equations x'(t)=f(xt){x'(t)=f(x_t)} we construct a continuous semiflow of continuously differentiable solution operators x0xt{x_0 \to x_t}, t0{t \le 0}, on open subsets of the Frechet space C((-,0],Rn){C((-\infty, 0], R^n)}. For nonautonomous equations this yields a continuous process of differentiable solution operators. As an application, we obtain processes which incorporate all solutions of Volterra integro-differential equations x'(t)=∫0tk(t,s)h(x(s))ds{x'(t)={\int_0}^t k(t,s) h(x(s)) ds}.
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Awan, Muhammad, Muhammad Noor, Marcela Mihai, and Khalida Noor. "Two point trapezoidal like inequalities involving hypergeometric functions." Filomat 31, no. 8 (2017): 2281–92. http://dx.doi.org/10.2298/fil1708281a.
In this paper, we derive a new integral identity for differentiable function. Using this new integral identity as an auxiliary result, we derive some new two point trapezoidal like inequalities for differentiable harmonic h-convex functions. These inequalities can also be viewed as Hermite-Hadamard type inequalities. We also discuss some new special cases which can be deduced from our main results.
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Latif, Muhammad Amer. "New Weighted Hermite–Hadamard Type Inequalities for Differentiable h -Convex and Quasi h -Convex Mappings." Journal of Mathematics 2021 (July 5, 2021): 1–14. http://dx.doi.org/10.1155/2021/4495588.
In this paper, new weighted Hermite–Hadamard type inequalities for differentiable h -convex and quasi h -convex functions are proved. These results generalize many results proved in earlier works for these classes of functions. Applications of some of our results to s ˘ -divergence and to statistics are given.
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Gaydu, M., M. H. Geoffroy, and C. Jean-Alexis. "An inverse mapping theorem for H-differentiable set-valued maps." Journal of Mathematical Analysis and Applications 421, no. 1 (January 2015): 298–313. http://dx.doi.org/10.1016/j.jmaa.2014.07.006.
Ce travail vise à étendre la représentation variationnelle classique du logarithme de l’espérance de e−f par rapport à la mesure de Wiener à des mesures plus générales. Nous donnons d’abord une condition suffisante de différentiabilité forte sur l’espace de Cameron-Martin. Dans un second temps nous étendons la formulation variationnelle à la mesure image d’une diffusion, puis nous utilisons cet exemple pour généraliser la représentation à un large ensemble de mesure. Nous diminuons aussi les hypothèses d’intégrabilité sur f et prouvons de nouveaux résultats sur l’inversibilité stochastique et l’existence de solutions fortes pour certaines équations différentielles stochastiques. Finalement, nous étendons encore une fois la représentation This work aims at extending the classical variational formulation of the logarithm of the expectation of e −f with respect to the Wiener measure to more general measures. First we give a sufficient criteria for functions to be strongly differentiable over the Cameron-Martin space. Then we extend the variational formulation to the case of the image measure of a diffusion, and we use this example to generalize the variational formulation to a wide set of measures, while reducing the integrability hypothesis over f and obtaining new results concerning stochastic invertibility and existence of strong solutions of stochastic differential equations. Finally, we extend once more this formulation by considering conditional expectations with respect to the same set of measures
Книги з теми "H-differentiable":
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Mishachev, N., and Y. Eliashberg. Introduction to the $h$-Principle (Graduate Studies in Mathematics, V 48). American Mathematical Society, 2002.
Kashuri, Artion, and Rozana Liko. "Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Generalized ((h 1, h 2); (η 1, η 2))-Convex Mappings and Their Applications." In Frontiers in Functional Equations and Analytic Inequalities, 469–88. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28950-8_24.
Horsfield, A. P. "A computationally efficient differentiable Tight-Binding energy functional." In C,H,N and O in Si and Characterization and Simulation of Materials and Processes, 219–23. Elsevier, 1996. http://dx.doi.org/10.1016/b978-0-444-82413-4.50113-x.
Тези доповідей конференцій з теми "H-differentiable":
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Emharuethai, Chanikan, and Piyapong Niamsup. "Robust H∞ control of linear systems with interval non-differentiable time-varying delays." In 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012). IEEE, 2012. http://dx.doi.org/10.1109/wcica.2012.6358117.
