Coefficient bounds for certain subclasses of bi-univalent functions

Author: È˜ahsene AltÄ±nkaya / Sibel YalÃ§Ä±n

Abstract: In this paper we discuss some newly constructed subclasses of
bi-univalent functions and establish bounds for the
coefficients of the functions in the subclasses $S_{\Sigma }(\lambda ,\alpha )$ and
$S_{\Sigma }(\lambda ,\beta ). $
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Abstract: To study approximation properties of linear positive operators various identities involving divided differences are used. The aim of this note is to present two types of such kind of identities. The first one was used by Abel and Ivan [Abel, U. and Ivan, M., Some identities for the operator of Bleimamm, Butzer and Hahn
involving divided differences, Calcolo, 36 (1999), 143--160; Abel, U. and Ivan, M., New representation of the remainder in the Bernstein approximation, J. Math. Anal. Appl., 381 (2011), No. 2, 952--956] to derive approximation properties of Bleimann, Butzer and Hahn (BBH) operators from the corresponding properties of the classical Bernstein operators.
The second type of identifies can be used to derive some approximation properties of the BBH operators from the properties of some Stancu type operators.
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A numerical study on the robustness and efficiency of the PL homotopy algorithm for solving unconstrained optimization problems

Author: Andrei Bozântan / Vasile Berinde

Abstract: Our aim in this paper is to illustrate the relevance of the fixed point piecewise-linear homotopy algorithm
for solving unconstrained optimization problems. The numerical tests are performed by using an implementation of the piecewise-linear homotopy algorithm in the modern programming language C#, as described previously in [Bozantan, A., An implementation of the piecewise-linear homotopy algorithm for the computation of fixed points, Creat. Math. Inform., 19 (2010), No.2, 140--148] and [Bozantan, A. and Berinde, V., Applications of the PL homotopy algorithm for the computation of fixed points to unconstrained optimization problems, Creat. Math. Inform., 22 (2013), No. 1, 41--46]. As shown by the numerical experiments done on a set of classic test functions in optimization theory, the PL homotopy algorithm appears to be more reliable than the classical Newton's method and some other important methods for finding local or global minima.
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Interactive dynamic tests for evaluating the development of spatial abilities in high school

Author: LÃ¡szlÃ³ Budai

Abstract: In the last 10-15 years the number of studies examining spatial abilities of students has increased rapidly. The development of the spatial ability system components is important since these skills are used in everyday life and in order to reach our goal (position) people need good spatial perception in many cases. Geo-Gebra is a suitable and effective tool for developing these abilities. New methods for measuring these abilities can be developed that would be better adapted to today's needs. The dynamic and interactive adaptation of available GeoGebra tests for measuring spatial abilities would place these measurements on a new ground. However, there are many unanswered questions. The technical background, results and experiences of pilot a test of these methods are presented here.
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On the equal variables method applied to real variables

Author: Vasile Cârtoaje

Abstract: As it is known, the equal variables method can be used to create and solve difficult symmetric inequalities in nonnegative variables involving the expressions $x_1+x_2+\cdots+x_n$, $x_1^k+x_2^k+\cdots+x_n^k$ and $f(x_1)+f(x_2)+\cdots+f(x_n)$, where $k$ is a real constant, and $f$ is a differentiable function on $(0,\infty)$ such that $g(x)=f'(x^{\frac 1{k-1}})$ is strictly convex. In this paper, we extend the equal variables method to real variables.
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About the radius of convexity of some analytic functions

Author: Olga Engel / PÃ¡l A. KupÃ¡n / Ãgnes O. PÃ¡ll- SzabÃ³

Abstract: In this paper we prove a general result regarding the radius of convexity for different particular functions. The method of convolutions is used. The results are applied to deduce sharp bounds regarding functions, which satisfy differential subordinations.
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A hybrid iterative method without extrapolating step for solving mixed equilibrium problem

Author: K. R. Kazmi / S. H. Rizvi / Rehan Ali

Abstract: In this paper, we introduce a hybrid iterative method without extrapolating step to approximate a solution of mixed equilibrium problem in real Hilbert space. We prove a strong convergence theorem for the sequences generated by the proposed iterative algorithm. The result presented in this paper is the extension and generalization of the previously known results in this area.
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Kannan contractions and strongly demicontractive mappings

Author: Ștefan Mărușter / Ioan A. Rus

Abstract: Inclusion relations between strongly demicontractive mappings, quasi $(L, m)$-contractions, and Kannan contractions are established. As corollaries, $T$-stability and strong convergence of Picard and Mann iterations for strongly demicontractive mappings are obtained.
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Remark on the Laplacian-energy-like and Laplacian incidence energy invariants of graphs

Author: I. Å½. MilovanoviÄ‡ / E. I. MilovanoviÄ‡ / M. R. PopoviÄ‡ / R. M. StankoviÄ‡

Abstract: Let $G$ be an undirected connected graph with $n$ vertices and $m$ edges, $n\ge 3$, and let $\mu_1\ge \mu_2 \ge \cdots \ge \mu_{n-1}>\mu_n =0$ and $\rho_1\ge \rho_2\ge \cdots \ge \rho_{n-1} >\rho_n =0$ be Laplacian and normalized Laplacian eigenvalues of $G$, respectively. The Laplacian-energy-like (LEL) invariant of graph $G$ is defined as $\rm LEL(G)=\sum_{i=1}^{n-1}\sqrt{\mu_i}$. The Laplacian incidence energy of graph is defined as $\rm LIE(G)=\sum_{i=1}^{n-1}\sqrt{\rho_i}$. In this paper, we consider lower bounds of graph invariants $\rm LEL(G)$ and $\rm LIE(G)$ in terms of some graph parameters, that refine some known results.
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Abstract: In this paper we define a new type of connectedness by using $b$ - open sets and discuss the relationship between this connectedness and various types of connectedness already defined in topological spaces.
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A new Hermite-Hadamard type inequality for $h$-convex functions

Author: Muhammad Aslam Noor / Khalida Inayat Noor / Muhammad Uzair Awan

Abstract: In this paper, we derive a new refinement of Hermite-Hadamard
inequality for the class of $h$-convex functions. We also discuss
some new and known special cases which can be obtained from our main
results. Results obtained in this paper may be viewed as significant
improvement of the known results.
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Some conjugate WP-Bailey pairs and transformation formulas for $q$-series

Author: H. M. Srivastava / S. N. Singh / S. P. Singh / Vijay Yadav

Abstract: In this paper, the authors prove several theorems
involving $q$-series identities by applying a
certain family of conjugate WP-Bailey pairs.
Making use of these theorems in conjunction with
some WP-Bailey pairs, various transformation
formulas for $q$-series are also established.
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Some univalence criteria for a family of integral operators

Author: Virgil Pescar / Laura Stanciu

Abstract: The main objective of this paper is to obtain sufficient
conditions for a family of integral operators to be univalent in
the open unit disk $\mathcal{U},$ using new results on univalence
of analytic functions. These integral operators were considered in
a recent work, see [Stanciu, L., The univalence conditions of some integral operators,
Abstr. Appl. Anal., 2012, Art. ID 924645, 9 pp.].
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Abstract: This article is proposing an appropriate approach to solve a constrained multi objective model by using the theory of utility functions in fuzzy form. One of the approaches to optimize a multi objective mathematical model is to employ utility functions for the objectives. Recent studies on utility based multi objective optimization concentrate on considering just one utility function for each objective. But, in reality it is not reasonable to have a unique utility function corresponding to each objective function. Here, a constrained multi objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective and the total utility function of the problem will be a fuzzy nonlinear mathematical model. Since there are not any conventional approaches to solve such a model, a defuzzification method to change the total utility function to a crisp nonlinear model is employed. Meanwhile, $\alpha $-cut method is applied to defuzzify the conditional utility functions. This action results in changing the total utility function to a crisp single objective nonlinear model and will simplify the optimization process of the total utility function. The effectiveness of the proposed approach is shown by solving a test problem.
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