Solutions of equivariance for a polynomial-like iterative equation

2000 ◽  
Vol 130 (5) ◽  
pp. 1153-1163 ◽  
Author(s):  
Weinian Zhang
Keyword(s):  
Fixed Point ◽  
Euclidean Space ◽  
Closed Subgroup ◽  
General Linear Group ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Dimensional Euclidean Space ◽  
Continuous Solutions ◽  
Iterative Equation ◽  
Higher Dimensional

Using fixed point theorems we discuss continuous solutions of Γ-equivariance for a polynomial-like iterative equation on the real line, where Γ is a closed subgroup of the general linear group GL(R). Our main results guarantee the existence of solutions with certain kinds of symmetry. We show that, under restrictive hypotheses, similar results can be proved in a higher-dimensional case, where the symmetry group is a topologically finitely generated subgroup of the group generated by rotations and dilations in N-dimensional Euclidean space.

scholarly journals The mathematical foundations of anelasticity: existence of smooth global intermediate configurations

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200462
Author(s):  
Christian Goodbrake ◽  
Alain Goriely ◽  
Arash Yavari
Keyword(s):  
Euclidean Space ◽  
Deformation Gradient ◽  
Deformation Tensor ◽  
Dimensional Euclidean Space ◽  
Multiplicative Decomposition ◽  
Mathematical Basis ◽  
Isometric Embeddings ◽  
Higher Dimensional ◽  
Mathematical Foundations ◽  
Central Tool

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.

scholarly journals On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1084 ◽  
Author(s):  
Bashir Ahmad ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas ◽  
Hamed H. Al-Sulami
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Multivalued Maps ◽  
Functional Differential ◽  
Functional Differential Inclusions

We prove the existence of solutions for neutral functional differential inclusions involving Hadamard fractional derivatives by applying several fixed point theorems for multivalued maps. We also construct examples for illustrating the obtained results.

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

scholarly journals Existence of Solutions ofα∈(2,3]Order Fractional Three-Point Boundary Value Problems with Integral Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
N. I. Mahmudov ◽  
S. Unul
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Integral Conditions ◽  
Uniqueness Of Solutions ◽  
Fractional Differential ◽  
Derivatives Of

Existence and uniqueness of solutions forα∈(2,3]order fractional differential equations with three-point fractional boundary and integral conditions involving the nonlinearity depending on the fractional derivatives of the unknown function are discussed. The results are obtained by using fixed point theorems. Two examples are given to illustrate the results.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations withp-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.

scholarly journals Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
H. M. Srivastava ◽  
Sachin V. Bedre ◽  
S. M. Khairnar ◽  
B. S. Desale
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Lower Solution ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Normed Linear Spaces ◽  
Monotonicity Conditions

Some hybrid fixed point theorems of Krasnosel’skii type, which involve product of two operators, are proved in partially ordered normed linear spaces. These hybrid fixed point theorems are then applied to fractional integral equations for proving the existence of solutions under certain monotonicity conditions blending with the existence of the upper or lower solution.

scholarly journals Existence of solutions for a fractional nonlocal boundary value problem

2020 ◽  
Vol 36 (3) ◽  
pp. 453-462
Author(s):  
RODICA LUCA
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Fractional Integrals ◽  
Nonlocal Boundary Value Problem ◽  
Fractional Differential

We investigate the existence of solutions for a Riemann-Liouville fractional differential equation with a nonlinearity dependent of fractional integrals, subject to nonlocal boundary conditions which contain various fractional derivatives and Riemann-Stieltjes integrals. In the proof of our main results we use different fixed point theorems.

scholarly journals Some New Fixed Point Theorems in b-Metric Spaces with Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 725
Author(s):  
Badriah A. S. Alamri ◽  
Ravi P. Agarwal ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Contraction Mappings ◽  
New Class

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results.

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