scholarly journals Ppf dependent fixed point results for hybrid rational and Suzuki-Edelstein type contractions in Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1339-1351 ◽  
Author(s):  
V. Parvaneh ◽  
H. Hosseinzadeh ◽  
N. Hussain ◽  
Lj. Ciric
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Coincidence Point ◽  
Periodic Boundary Value Problem ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Optim Theory

In this paper we introduce new notions of hybrid rational Geraghty and Suzuki-Edelstein type contractive mappings and investigate the existence and uniqueness of PPF dependent fixed point for such mappings in the Razumikhin class, where domain and range of the mappings are not the same. As an application of our PPF dependent fixed point results, we deduce corresponding PPF dependent coincidence point results in the Razumikhin class. Our results extend and improve the results of Sintunavarat and Kumam [J. Nonlinear Anal. Optim.: Theory Appl., Vol. 4, (2013), 157-162], Bernfeld, Lakshmikantham and Reddy [Applicable Anal., 6(1977), 271-280] and others. As an application of our results, we establish PPF dependent solution of a periodic boundary value problem.

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

scholarly journals On Solution of Boundary Value Problems via Weak Contractions

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Gopi Prasad ◽  
Hüseyin Işik
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Binary Relation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Result ◽  
Contractive Type

The aim is to present a new relational variant of fixed point result that generalizes various fixed point results of the existing theme for contractive type mappings. As an application, we solve a periodic boundary value problem and validate all assertions with the help of nontrivial examples. We also highlight the close connections of the fixed point results equipped with a binary relation to that of graph related metrical fixed point results. Radically, these investigations unify the theory of metrical fixed points for contractive type mappings.

scholarly journals Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

2020 ◽  
Vol 25 (2) ◽  
Author(s):  
Ehsan Pourhadi ◽  
Reza Saadati ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Expansion Condition

In this paper, inspired by the idea of Meir–Keeler contractive mappings, we introduce Meir–Keeler expansive mappings, say MKE, in order to obtain Krasnosel’skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir–Keeler mapping and expansive Krasnosel’skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel’skii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7–8):3229–3239, 2009].

scholarly journals Fixed point theorems via w-distance in relational metric spaces with an application

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1889-1898
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Binary Relation ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
First Order ◽  
Contractive Mappings

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance on metric spaces endowed with an arbitrary binary relation. Our fixed point theorems generalize recent results of Senapati and Dey [ J. Fixed Point Theory Appl., 19, 2945-2961, (2017)] and many other important results of the existing literature. Moreover, in order to revel the usability of our findings an example and an application to first order periodic boundary value problem are given.

scholarly journals Existence of Solutions for a Periodic Boundary Value Problem via Generalized Weakly Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sirous Moradi ◽  
Erdal Karapınar ◽  
Hassen Aydi
Keyword(s):  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Weakly Contractive

We discuss the existence of solutions for a periodic boundary value problem and for some polynomials. For this purpose, we present some fixed point theorems for weakly and generalized weakly contractive mappings in the setting of partially ordered complete metric spaces.

scholarly journals A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 50
Author(s):  
Based Ali ◽  
Mohammad Imdad ◽  
Salvatore Sessa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Symmetric Spaces ◽  
Periodic Boundary ◽  
Type Theorem ◽  
Comparison Functions ◽  
Uniqueness Of A Solution ◽  
Transitive Binary Relation

In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with a locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. In addition, we adopt an example to substantiate the genuineness of our newly proved result. Finally, as an application of our main result, we establish the existence and uniqueness of a solution of a periodic boundary value problem.

scholarly journals Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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