Existence of solutions of cantilever beam problem via (α-β-FG)-contractions in b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3057-3074 ◽  
Author(s):  
Hemant Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Periodic Point ◽  
Cantilever Beam ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Sufficient Conditions

In this work, our intention is to introduce the notion of rational (?-?-FG)-contraction mapping in b-metric-like spaces, and produce relevant fixed point and periodic point results for weakly ?-admissible mappings. Ulam-Hyers stability of this problem is also investigated. To illustrate our results, we give throughout the paper some examples, in particular in order to justify the use of rational terms. As an application, we obtain sufficient conditions for the existence of solutions for Cantilever Beam Problem.

scholarly journals Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wiyada Kumam ◽  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Point Boundary ◽  
Coupled Fixed Point Theorem ◽  
Fractional Differential

We study sufficient conditions for existence of solutions to the coupled systems of higher order hybrid fractional differential equations with three-point boundary conditions. For this motive, we apply the coupled fixed point theorem of Krasnoselskii type to form adequate conditions for existence of solutions to the proposed system. We finish the paper with suitable illustrative example.

scholarly journals Existence of solutions for impulsive fractional integrodifferential equations involving Gronwall’s inequality in Banach spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 115-122
Author(s):  
A. AL-OMARI ◽  
◽  
M. H. M. RASHID ◽  
K. KARTHIKEYAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Caputo Derivative ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Gronwall’S Inequality ◽  
Mild Conditions

In this paper, we study boundary value problems for impulsive fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

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.

scholarly journals On a nonlocal Cauchy problem for differential inclusions

2004 ◽  
Vol 2004 (5) ◽  
pp. 425-434 ◽  
Author(s):  
E. Gatsori ◽  
S. K. Ntouyas ◽  
Y. G. Sficas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Nonlocal Cauchy Problem

We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

Almost periodic solution of Nicholson's blowflies model with linear harvesting term and impulsive effects

2015 ◽  
Vol 08 (03) ◽  
pp. 1550053
Author(s):  
Zhijian Yao
Keyword(s):  
Fixed Point ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Nicholson’S Blowflies Model ◽  
Linear Harvesting Term

This paper is concerned with impulsive Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional.

scholarly journals Study on the Existence of Solutions for a Class of Nonlinear Neutral Hadamard-Type Fractional Integro-Differential Equation with Infinite Delay

2021 ◽  
Vol 5 (2) ◽  
pp. 52
Author(s):  
Kaihong Zhao ◽  
Yue Ma
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Normed Space ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The existence of solutions for a class of nonlinear neutral Hadamard-type fractional integro-differential equations with infinite delay is researched in this paper. By constructing an appropriate normed space and utilizing the Banach contraction principle, Krasnoselskii’s fixed point theorem, we obtain some sufficient conditions for the existence of solutions. Finally, we provide an example to illustrate the validity of our main results.

scholarly journals A fixed point problem under a finite number of equality constraints on b-Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5837-5849
Author(s):  
Monica-Felicia Bota ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Finite Number ◽  
Banach Spaces ◽  
Metric Space ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Equality Constraints ◽  
Point Problem

In this manuscript, we investigate a fixed point problem under a finite number of equality constraints involving a well-known Ciric type mappings in the context of b-metric space. We obtain sufficient conditions for the existence of solutions of such problems. We also express some immediate consequences of our main results.

scholarly journals Solutions of nonlinear difference equations in the domain of $(\zeta _{n})$-Cesàro matrix in $\ell _{t(\cdot)}$ of nonabsolute type, and its pre-quasi ideal

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Fixed Point ◽  
Difference Equations ◽  
Sequence Space ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Operator Ideal ◽  
Topological Properties ◽  
Nonlinear Difference Equations ◽  
Cesàro Matrix ◽  
Eigenvalues Distribution

AbstractWe have constructed the sequence space $(\Xi (\zeta ,t) )_{\upsilon }$ ( Ξ ( ζ , t ) ) υ , where $\zeta =(\zeta _{l})$ ζ = ( ζ l ) is a strictly increasing sequence of positive reals tending to infinity and $t=(t_{l})$ t = ( t l ) is a sequence of positive reals with $1\leq t_{l}<\infty $ 1 ≤ t l < ∞ , by the domain of $(\zeta _{l})$ ( ζ l ) -Cesàro matrix in the Nakano sequence space $\ell _{(t_{l})}$ ℓ ( t l ) equipped with the function $\upsilon (f)=\sum^{\infty }_{l=0} ( \frac{ \vert \sum^{l}_{z=0}f_{z}\Delta \zeta _{z} \vert }{\zeta _{l}} )^{t_{l}}$ υ ( f ) = ∑ l = 0 ∞ ( | ∑ z = 0 l f z Δ ζ z | ζ l ) t l for all $f=(f_{z})\in \Xi (\zeta ,t)$ f = ( f z ) ∈ Ξ ( ζ , t ) . Some geometric and topological properties of this sequence space, the multiplication mappings defined on it, and the eigenvalues distribution of operator ideal with s-numbers belonging to this sequence space have been investigated. The existence of a fixed point of a Kannan pre-quasi norm contraction mapping on this sequence space and on its pre-quasi operator ideal formed by $(\Xi (\zeta ,t) )_{\upsilon }$ ( Ξ ( ζ , t ) ) υ and s-numbers is presented. Finally, we explain our results by some illustrative examples and applications to the existence of solutions of nonlinear difference equations.

scholarly journals Existence and well-posedness for excess demand equilibrium problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lam Quoc Anh ◽  
Pham Thanh Duoc ◽  
Tran Quoc Duy
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Excess Demand ◽  
Well Posedness ◽  
Euclidean Spaces

<p style='text-indent:20px;'>In this paper, we study excess demand equilibrium problems in Euclidean spaces. Applying the Glicksberg's fixed point theorem, sufficient conditions for the existence of solutions for the reference problems are established. We introduce a concept of well-posedness, say Levitin–Polyak well-posedness in the sense of Painlevé–Kuratowski, and investigate sufficient conditions for such kind of well-posedness.</p>

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