scholarly journals A Generalization of Nadler’s Fixed Point Theorem

2017 ◽  
Vol 72 (3) ◽  
pp. 1525-1534 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nadler’S Fixed Point Theorem

scholarly journals Some new coincidence point results for single-valued and multi-valued mappings in $b$-metric spaces via digraphs

2020 ◽  
Vol 53 (1) ◽  
pp. 69-84
Author(s):  
S. K. Mohanta ◽  
R. Kar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Nadler’S Fixed Point Theorem

We introduce the concept of generalized $F$-$G$-contraction and prove some new coincidence point results for single-valued and multi-valued mappings in $b$-metric spaces endowed with a digraph $G$. Our results generalize and extend several well-known comparable results including Nadler's fixed point theorem for multi-valued mappings. Moreover, we give some examples to justify the validity of our main result.

Some fixed point theorems for multi-valued mappings in graphical metric spaces

2020 ◽  
Vol 70 (3) ◽  
pp. 719-732
Author(s):  
Satish Shukla ◽  
Hans-Peter A. Künzi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Nadler’S Fixed Point Theorem

AbstractIn this paper, we discuss some topological properties of graphical metric spaces and introduce the G-set metric with respect to a graphical metric. Some fixed point results are introduced which generalize the famous Nadler’s fixed point theorem.

scholarly journals Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
N. Hussain ◽  
I. Iqbal ◽  
Badriah A. S. Alamri ◽  
M. A. Kutbi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Nadler’S Fixed Point Theorem ◽  
Proper Generalization

In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.

scholarly journals New Results and Generalizations for Approximate Fixed Point Property and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Farshid Khojasteh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Fixed Point Property ◽  
Point Property ◽  
Approximate Fixed Point ◽  
Nadler’S Fixed Point Theorem ◽  
Approximate Fixed Point Property

We first introduce the concept of manageable functions and then prove some new existence theorems related to approximate fixed point property for manageable functions andα-admissible multivalued maps. As applications of our results, some new fixed point theorems which generalize and improve Du's fixed point theorem, Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and Nadler's fixed point theorem and some well-known results in the literature are given.

scholarly journals A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 478 ◽  
Author(s):  
Nayab Alamgir ◽  
Quanita Kiran ◽  
Hassen Aydi ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Nadler’S Fixed Point Theorem

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi–Takahashi’s type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature.

scholarly journals Generalized Ekeland’s variational principle with applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Eshagh Hashemi ◽  
Reza Saadati ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Fixed Point Theorem ◽  
Equilibrium Problem ◽  
Point Theorem ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Nadler’S Fixed Point Theorem

Abstract By using the concept of Γ-distance, we prove EVP (Ekeland’s variational principle) on quasi-F-metric (q-F-m) spaces. We apply EVP to get the existence of the solution to EP (equilibrium problem) in complete q-F-m spaces with Γ-distances. Also, we generalize Nadler’s fixed point theorem.

scholarly journals Set-Valued Hardy-Rogers Type Contraction in 0-Complete Partial Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Satish Shukla ◽  
Stojan Radenović ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Partial Metric ◽  
Nadler’S Fixed Point Theorem ◽  
Partial Metric Spaces ◽  
Type Contraction

In this paper we introduce set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces and prove the corresponding theorem of fixed point. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by Aydi et al. (2012). As an application of our results, a homotopy theorem for such mappings is derived. Also, some examples are included which show that our generalization is proper.

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