<abstract xmlns="http://www.w3.org/1999/xhtml">Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear <italic>nth</italic> 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 <italic>nth</italic> 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.</abstract>

Department of Humanities and Social Sciences

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

Department of Mathematical and Computational Sciences, National Institute of Technology

Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we intend to study three concepts of (<italic>h, k</italic>)-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.</abstract>

Faculty of Mathematics and Computer Science

Faculty of Social Science, Humanities and Physical Education and Sports

“Vasile Goldiş” Western University of Arad

Splitting with Different Growth Rates for Linear Discrete-time Skew-evolution Semiflows in Banach Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper we study <italic>η</italic>-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider <italic>η</italic>-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study <italic>φ</italic>-Ricci symmetric <italic>η</italic>-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition <italic>R.R</italic> = <italic>Q</italic>(<italic>S, R</italic>)is considered. Finally, an example is constructed to prove the existence of a proper <italic>η</italic>-Ricci soliton on a Kenmotsu 3-manifold.</abstract>

<italic>η</italic>-Ricci Solitons on Kenmotsu 3-Manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">For a single valued mapping <italic>T</italic> in a <italic>G</italic>-complete <italic>G-</italic>metric space (<italic>X, d</italic>), we show that if <italic>Tn</italic>,for some <italic>n></italic> 1, is a contraction, then <italic>T</italic> itself is a contraction under another related <italic>G</italic>-metric <italic>d</italic>′. We establish moreover that if <italic>T</italic> is uniformly continuous, then <italic>d</italic>′ is <italic>G</italic>-complete.</abstract>

Institut de Mathématiques et de Sciences Physiques (IMSP)

African Center for Advanced Studies (ACAS)

Related <italic>G</italic>-metrics and Fixed Points

<abstract xmlns="http://www.w3.org/1999/xhtml">The object of the present paper is to study <italic>η</italic>-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.</abstract>

<italic>η</italic>-Ricci Solitons on Quasi-Sasakian Manifolds

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

<abstract xmlns="http://www.w3.org/1999/xhtml">Let (<italic>M, g</italic>) be any compact, connected, Riemannian manifold of dimension <italic>n</italic>. We use a transport of measures and the barycentre to construct a map from (<italic>M, g</italic>) onto a Hyperbolic manifold (ℍ<italic>n/</italic>Λ, <italic>g</italic>0) (Λ is a torsionless subgroup of <italic>Isom</italic>(ℍ<italic>n,g</italic>0)), in such a way that its jacobian is sharply bounded from above. We make no assumptions on the topology of (<italic>M, g</italic>) and on its curvature and geometry, but we only assume the existence of a measurable Gromov-Hausdorff <italic>ε</italic>-approximation between (ℍ<italic>n/</italic>Λ, <italic>g</italic>0) and (<italic>M, g</italic>). When the Hausdorff approximation is continuous with non vanishing degree, this leads to a sharp volume comparison, if <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2018-0008_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>ɛ</mi><mo>&lt;</mo><mfrac><mn>1</mn><mrow><mn>64</mn><mi> </mi><msup><mrow><mi>n</mi></mrow><mn>2</mn></msup></mrow></mfrac><mtext>min</mtext><mrow><mo>(</mo><mrow><msub><mrow><mi>inj</mi></mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>ℍ</mi></mrow><mi>n</mi></msup><mo>/</mo><mi>Λ</mi><mo>,</mo><msub><mrow><mi>g</mi></mrow><mn>0</mn></msub></mrow><mo>)</mo></mrow></mrow></msub><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></math><tex-math>$\varepsilon &lt; {1 \over {64\,{n^2}}}\min \left( {in{j_{\left( {{{\Bbb H}^n}/\Lambda ,{g_0}} \right)}},1} \right)$</tex-math></alternatives></inline-formula>, then
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_awutm-2018-0008_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mtable><mtr><mtd><mrow><mi>Vol</mi><mrow><mo>(</mo><mrow><msup><mrow><mi>M</mi></mrow><mi>n</mi></msup><mo>,</mo><mi>g</mi></mrow><mo>)</mo></mrow><mo>≥</mo></mrow></mtd></mtr><mtr><mtd><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><mn>160</mn><mi>n</mi><mrow><mo>(</mo><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mo>)</mo></mrow><msqrt><mrow><mfrac><mi>ɛ</mi><mrow><mtext>min</mtext><mrow><mo>(</mo><mrow><msub><mrow><mi>inj</mi></mrow><mrow><mrow><mo>(</mo><mrow><msup><mrow><mi>H</mi></mrow><mi>n</mi></msup><mo>/</mo><mi>Λ</mi><mo>,</mo><msub><mrow><mi>g</mi></mrow><mn>0</mn></msub></mrow><mo>)</mo></mrow></mrow></msub><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mfrac><mi>n</mi><mn>2</mn></mfrac></mrow></msup><mrow><mo>|</mo><mrow><mi>deg</mi><mi> </mi><mi>h</mi></mrow><mo>|</mo></mrow><mo>⋅</mo><mi>Vol</mi><mrow><mo>(</mo><mrow><msup><mrow><mi>X</mi></mrow><mi>n</mi></msup><mo>,</mo><msub><mrow><mi>g</mi></mrow><mn>0</mn></msub></mrow><mo>)</mo></mrow><mo>.</mo></mrow></mtd></mtr></mtable></mrow></math><tex-math>$$\matrix{{Vol\left( {{M^n},g} \right) \ge }\cr {{{\left( {1 + 160n\left( {n + 1} \right)\sqrt {{\varepsilon \over {\min \left( {in{j_{\left( {{{\Bbb H}^n}/\Lambda ,{g_0}} \right)}},1} \right)}}} } \right)}^{{n \over 2}}}\left| {\deg \,h} \right| \cdot Vol\left( {{X^n},{g_0}} \right).} \cr }$$</tex-math></alternatives></disp-formula></abstract>

Volume Comparison in the presence of a Gromov-Hausdorff <italic>ε−</italic>approximation II

<abstract xmlns="http://www.w3.org/1999/xhtml">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 <xref ref-type="bibr" rid="j_awutm-2018-0009_ref_016_w2aab3b7b8b1b6b1ab1ac16Aa">[16]</xref> (Comm. Math. Res. 31(2015), 149-160) and many others.</abstract>

Department of Mathematics, Govt. N. P. G., College of Science

Department of Mathematics, Govt. Kaktiya P. G. College

Strong Convergence Theorems for Hybrid Mixed Type Nonlinear Mappings in Banach Spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">The object of the present paper is to study Ricci soliton in <italic>β</italic>-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a <italic>β</italic>-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒ<italic>Vg</italic> +2<italic>S</italic>)is ∇-parallel where <italic>V</italic> is a given vector field, then the structure (<italic>g, V, λ</italic>) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in <italic>β</italic>-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional <italic>β</italic>-Kenmotsu manifold are discussed with an example.</abstract>

Ricci Solitons in <italic>β</italic>-Kenmotsu Manifolds

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Annals of West University of Timisoara - Mathematics and Computer Science

Volume 56 (2018): Issue 1 (July 2018)

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Local Convergence Analysis of an Efficient Fourth Order Weighted-Newton Method under Weak Conditions

Splitting with Different Growth Rates for Linear Discrete-time Skew-evolution Semiflows in Banach Spaces

η-Ricci Solitons on Kenmotsu 3-Manifolds

Related G-metrics and Fixed Points

η-Ricci Solitons on Quasi-Sasakian Manifolds

Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

Volume Comparison in the presence of a Gromov-Hausdorff ε−approximation II

Strong Convergence Theorems for Hybrid Mixed Type Nonlinear Mappings in Banach Spaces

Ricci Solitons in β-Kenmotsu Manifolds

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