scholarly journals Common Fixed Points of (α,η) − (θ,ϝ) Rational Contractions with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Periodic Problem ◽  
Elastic Beam ◽  
Common Fixed Points ◽  
First Order ◽  
Beam Equations ◽  
Nonlinear Elastic ◽  
Rational Contraction ◽  
Elastic Beam Equations

We present the notion of set valued (α,η)-(θ,ϝ) rational contraction mappings and then some common fixed point results of such mappings in the setting of metric spaces are established. Some examples are presented to support the concepts introduced and the results proved in this paper. These results unify, extend, and refine various results in the literature. Some fixed point results for both single and multivalued (θ,ϝ) rational contractions are also obtained in the framework of a space endowed with partial order. As application, we establish the existence of solutions of nonlinear elastic beam equations and first-order periodic problem.

scholarly journals The Existence of Symmetric Positive Solutions of Fourth-Order Elastic Beam Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 121 ◽  
Author(s):  
Münevver Tuz
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Point Theory ◽  
Beam Equations ◽  
Symmetric Positive Solutions ◽  
Elastic Beam Equations

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii.

scholarly journals MULTIPLE POSITIVE SOLUTIONS OF BVPS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-CARATHEODORY NONLINEARITIES

2014 ◽  
Vol 19 (3) ◽  
pp. 395-416 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Elastic Beam ◽  
Multiple Positive Solutions ◽  
Beam Equations ◽  
Carathéodory Function ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Elastic Beam Equations

In this article, the existence of multiple positive solutions of boundary-value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x, x′ and x″, f may be singular at t = 0 and t = 1 and f is non-Caratheodory function. The analysis relies on the well known Schauder fixed point theorem and the five functional fixed point theorems in the cones.

scholarly journals Common fixed points of (α-ψ)- generalized rational multivalued contractions in dislocated quasi b-metric spaces and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3263-3284 ◽  
Author(s):  
Mujahid Abbas ◽  
Vladimir Rakocevic ◽  
Bahru Leyew
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Continuous Solution ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Multivalued Operator ◽  
Multivalued Contractions ◽  
Rational Contraction

In this paper, the concept of (?-?)-generalized rational contraction multivalued operator is introduced and then the existence of common fixed points of such mapping in complete dislocated quasi bmetric spaces is obtained. Some examples are presented to show that the results proved herein are potential generalization and extension of comparable existing results in the literature. We also study Ulam-Hyers stability of fixed point problems of (?-?)-generalized rational contraction multivalued operator. We also obtain some common fixed point results for single and multivalued mappings in a complete dq b-metric space endowed with a partial order. As an application, the existence of a continuous solution of an integral equation under appropriate assumptions is obtained.

scholarly journals Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdullah Shoaib ◽  
Qasim Mahmood ◽  
Aqeel Shahzad ◽  
Mohd Salmi Md Noorani ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Rational Contraction ◽  
Rational Type

AbstractThe objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Variational approaches to impulsive elastic beam equations of Kirchhoff type

2016 ◽  
Vol 61 (7) ◽  
pp. 931-968 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Massimiliano Ferrara ◽  
Shahin Moradi
Keyword(s):  
Elastic Beam ◽  
Kirchhoff Type ◽  
Beam Equations ◽  
Variational Approaches ◽  
Elastic Beam Equations
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