scholarly journals Fixed Point Results for a Class of Monotone Nonexpansive Type Mappings in Hyperbolic Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Rameshwar Pandey ◽  
Rajendra Pant ◽  
Ahmed Al-Rawashdeh
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence Results ◽  
Hyperbolic Spaces ◽  
Iteration Algorithm ◽  
Nonlinear Integral Equations ◽  
Convergence Results ◽  
Partially Hyperbolic

We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mapping in partially hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative nontrivial examples have also been discussed. Finally, we provide an application of our results to nonlinear integral equations.

scholarly journals Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 281
Author(s):  
Rajendra Pant ◽  
Rameshwa Pandey
Keyword(s):  
Fixed Point ◽  
Existence Results ◽  
Hyperbolic Spaces ◽  
Iteration Algorithm ◽  
Convergence Results

<p>We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed.</p>

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

scholarly journals Fixed point theorems in Fréchet algebras and Fréchet spaces and applications to nonlinear integral equations

2017 ◽  
Vol 11 (2) ◽  
pp. 340-357 ◽  
Author(s):  
Szymon Dudek
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Fréchet Spaces ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness

In this paper, we present two new fixed point theorems in Fr?chet algebras and Fr?chet spaces. Our fixed point results are expressed with the help of family of measures of noncompactness and generalizes Darbo theorem. As an application, we establish some existence results for various types of nonlinear integral equations.

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).

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
JinRong Wang ◽  
Chun Zhu ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Order ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Limit Property ◽  
Type Integral

AbstractIn this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

scholarly journals Fixed Point Theorems for ${\mathscr{Z}}_{\vartheta}$ -Contraction and Applications to Nonlinear Integral Equations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 120023-120029
Author(s):  
Xiangling Li ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Ekrem Savas
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equations
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