Showing papers in "Annals of the West University of Timisoara: Mathematics and Computer Science in 2018"
Abstract: Abstract In this paper, we introduce and study the class of enriched strictly pseudocontractive mappings in Hilbert spaces and extend some convergence theorems, i.e., Theorem 12 in [Brow-der, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 3.1 in [Marino, G., Xu, H.-K., Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), no. 1, 336–346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.
13 citations
TL;DR: In this article, the concept of iterated function systems consisting of continuous functions satisfying Banach's orbital condition was introduced and it was shown that the fractal operator associated with such a system is weakly Picard.
Abstract: Abstract We introduce the concept of iterated function system consisting of continuous functions satisfying Banach’s orbital condition and prove that the fractal operator associated to such a system is weakly Picard. Some examples are provided.
6 citations
TL;DR: In this paper, the existence of a proper Ricci soliton on a Kenmotsu 3-manifold with Codazzi type of Ricci tensor is proved.
Abstract: Abstract In the present paper we study η-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider η-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study φ-Ricci symmetric η-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition R.R = Q(S, R)is considered. Finally, an example is constructed to prove the existence of a proper η-Ricci soliton on a Kenmotsu 3-manifold.
6 citations
TL;DR: In this paper, the existence results for a nonlinear Lyapunov matrix differential equation on ǫ are given using Banach and Schauder - Tychono fixed point theorems.
Abstract: Abstract Using Banach and Schauder - Tychono fixed point theorems, existence results for a nonlinear Lyapunov matrix differential equation on are given. The obtained results generalize and extend the results from [5] and [18].
5 citations
TL;DR: By using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rénye-Tsallis of order α entropies is studied.
Abstract: Abstract This paper studies, by using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rényi-Tsallis of order α entropies.
4 citations
3 citations
TL;DR: Nonlinear nth order FDEs are approximated, heuristically, on using Chebyshev neural network, which is a type of single layer functional link artificial neural network (FLANN) and explication of generalized Hukuhara differentiability (gH-differentiability) is added for the n fourth order differentiability of fuzzy-valued functions.
Abstract: Abstract Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the nth order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.
3 citations
TL;DR: In this paper, the Ricci soliton in β-Kenmotsu manifolds was studied and it was shown that if (ℒVg + 2S) is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci cositon.
Abstract: Abstract The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.
2 citations
TL;DR: In this article, it was shown that for a single valued mapping T in a G-complete G-metric space (X, d), if Tn, for some n> 1, is a contraction, then T itself is also a contraction under another related Gmetric d′.
Abstract: Abstract For a single valued mapping T in a G-complete G-metric space (X, d), we show that if Tn,for some n> 1, is a contraction, then T itself is a contraction under another related G-metric d′. We establish moreover that if T is uniformly continuous, then d′ is G-complete.
2 citations
2 citations
TL;DR: In this article, three concepts of (h, k)-splitting for skew-evolution semiflow, which model discrete-time variational systems in Banach spaces, are studied.
Abstract: Abstract In this paper we intend to study three concepts of (h, k)-splitting for skew-evolution semiflows, which model discrete-time variational systems in Banach spaces. We also aim to give connections between them, emphasized by counterexamples and we propose an open problem.
TL;DR: In this paper, a general concept of non-uniform (h, k)- dichotomy for evolution operators in Banach spaces is considered, and two characterizations of this concept in terms of some families of norms compatible with the dichotomy projectors are given.
Abstract: The paper considers a general concept of nonuniform (h; k)- dichotomy for evolution operators in Banach spaces. Two characterizations of this concept in terms of some families of norms compatible with the dichotomy projectors are given.
TL;DR: Wei and Guo as mentioned in this paper introduced a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two non-self mappings in the intermediate sense.
Abstract: Abstract In this paper, we introduce a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong convergence theorems for mentioned scheme and mappings in Banach spaces. Our results extend and generalize the corresponding results recently announced by Wei and Guo [16] (Comm. Math. Res. 31(2015), 149-160) and many others.
TL;DR: In this article, the authors use a transport of measures and the barycentre to construct a map from (M, g) onto a Hyperbolic manifold (Λ is a torsionless subgroup of Isom(ℍn,g0)), in such a way that its jacobian is sharply bounded from above.
Abstract: Abstract Let (M, g) be any compact, connected, Riemannian manifold of dimension n. We use a transport of measures and the barycentre to construct a map from (M, g) onto a Hyperbolic manifold (ℍn/Λ, g0) (Λ is a torsionless subgroup of Isom(ℍn,g0)), in such a way that its jacobian is sharply bounded from above. We make no assumptions on the topology of (M, g) and on its curvature and geometry, but we only assume the existence of a measurable Gromov-Hausdorff ε-approximation between (ℍn/Λ, g0) and (M, g). When the Hausdorff approximation is continuous with non vanishing degree, this leads to a sharp volume comparison, if ɛ<164 n2min(inj(ℍn/Λ,g0),1) $\\varepsilon < {1 \\over {64\\,{n^2}}}\\min \\left( {in{j_{\\left( {{{\\Bbb H}^n}/\\Lambda ,{g_0}} \\right)}},1} \\right)$ , then Vol(Mn,g)≥(1+160n(n+1)ɛmin(inj(Hn/Λ,g0),1))n2|deg h|⋅Vol(Xn,g0). $$\\matrix{{Vol\\left( {{M^n},g} \\right) \\ge }\\cr {{{\\left( {1 + 160n\\left( {n + 1} \\right)\\sqrt {{\\varepsilon \\over {\\min \\left( {in{j_{\\left( {{{\\Bbb H}^n}/\\Lambda ,{g_0}} \\right)}},1} \\right)}}} } \\right)}^{{n \\over 2}}}\\left| {\\deg \\,h} \\right| \\cdot Vol\\left( {{X^n},{g_0}} \\right).} \\cr }$$
TL;DR: In this paper, the authors studied the concept of uniform exponential trisplitting for skew-product semi-low in Banach spaces and obtained necessary and sufficient conditions for this concept of Datko's type.
Abstract: Abstract The aim of this paper is to study the concept of uniform exponential trisplitting for skew-product semiflow in Banach spaces. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. We obtain necessary and sufficient conditions for this concept of Datko’s type. a character-isation in terms of Lyapunov functions is provided. The results are obtained from the point of view of the projector families, i.e. invariant and strongly invariant.
TL;DR: In this paper, Sharma et al. used conditions only on the first derivative and proved the convergence of the method in [19] using conditions on derivatives upto the order five, they proved that the method is of order four.
Abstract: Abstract Local convergence analysis of a fourth order method considered by Sharma et. al in [19] for solving systems of nonlinear equations. Using conditions on derivatives upto the order five, they proved that the method is of order four. In this study using conditions only on the first derivative, we prove the convergence of the method in [19]. This way we extended the applicability of the method. Numerical example which do not satisfy earlier conditions but satisfy our conditions are presented in this study.
TL;DR: In this article, a Ricci tensor solitons in a 3-dimensional non-cosymplectic quasi-Sasakian manifold was studied and a particular type of second order parallel tensor in this manifold was considered.
Abstract: Abstract The object of the present paper is to study η-Ricci solitons in a 3-dimensional non-cosymplectic quasi-Sasakian manifolds. We study a particular type of second order parallel tensor in this manifold. Beside this we consider this manifold satisfying some curvature properties of Ricci tensor.
TL;DR: In this article, the Stirling's method is used to find fixed points of nonlinear operator equation and sufficient conditions are provided to study semilocal and local convergence of the method, where Lipschtiz continuity type conditions on the first Fréchet derivative of the operator are assumed.
Abstract: Abstract In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contractive conditions as in earlier works. This way expand the applicability of this method. Here we introduce a new type of majorizing sequences instead of usual majorizing sequences and recurrence relations. Finally the paper will be concluded with numerical examples and a favorable comparison with known results.