scholarly journals Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete b-Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ismat Beg ◽  
Gunaseelan Mani ◽  
Arul Joseph Gnanaprakasam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fixed Point ◽  
Unique Solution ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Generalized Orthogonal

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

scholarly journals Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 266 ◽  
Author(s):  
Piyachat Borisut ◽  
Poom Kumam ◽  
Vishal Gupta ◽  
Naveen Mani
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
Ordered Metric Spaces ◽  
First Order

A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

scholarly journals New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 324 ◽  
Author(s):  
Sujitra Sanhan ◽  
Winate Sanhan ◽  
Chirasak Mongkolkeha
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
Generalized Pseudodistance

The purpose of this article is to prove some existences of fixed point theorems for generalized F -contraction mapping in metric spaces by using the concept of generalized pseudodistance. In addition, we give some examples to illustrate our main results. As the application, the existence of the solution of the second order differential equation is given.

DERIVATION OF 2-POINT ZERO STABLENUMERICAL ALGORITHM OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 579-583
Author(s):  
Muhammad Abdullahi ◽  
Bashir Sule ◽  
Mustapha Isyaku
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Ordinary Differential Equation ◽  
Differentiation Formula ◽  
First Order ◽  
Backward Differentiation Formula

This paper is aimed at deriving a 2-point zero stable numerical algorithm of block backward differentiation formula using Taylor series expansion, for solving first order ordinary differential equation. The order and zero stability of the method are investigated and the derived method is found to be zero stable and of order 3. Hence, the method is suitable for solving first order ordinary differential equation. Implementation of the method has been considered

scholarly journals Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Mappings ◽  
Random Differential Equations ◽  
Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

scholarly journals On Some Interpolative Contractions of Suzuki Type Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Andreea Fulga ◽  
Seher Sultan Yeşilkaya
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Admissible Maps

The goal of this study is to propose a new interpolative contraction mapping by using an interpolative approach in the setting of complete metric spaces. We present some fixed point theorems for interpolative contraction operators using w -admissible maps which satisfy Suzuki type mappings. In addition, some results are given. These results generalize several new results present in the literature. Moreover, examples are provided to show the suitability of our given results.

scholarly journals Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b-Metric Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Budi Nurwahyu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weakly Compatible ◽  
Compatible Function ◽  
Function Property ◽  
The Common ◽  
Common Fixed Point Theorems

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property.

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