scholarly journals Solution to Fredholm integral inclusions via (F, δb)-contractions

2016 ◽  
Vol 14 (1) ◽  
pp. 1053-1064 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Ravi P. Agarwal ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Integral Inclusion

AbstractWe present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

scholarly journals Some New Fixed Point Theorems in b-Metric Spaces with Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 725
Author(s):  
Badriah A. S. Alamri ◽  
Ravi P. Agarwal ◽  
Jamshaid Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Contraction Mappings ◽  
New Class

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results.

scholarly journals Solutions to Fredholm Integral Inclusions via Generalized Fuzzy Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 808 ◽  
Author(s):  
Hamed H Al-Sulami ◽  
Jamshaid Ahmad ◽  
Nawab Hussain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Unknown Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Multivalued Operator ◽  
Complete Metric Spaces ◽  
New Class ◽  
Integral Inclusion ◽  
The Family

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , φ ( s ) ) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
R. K. Sharma ◽  
Sumit Chandok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Contraction Mappings ◽  
Integro Differential Equation

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ -contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam’s stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.

scholarly journals Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wiyada Kumam ◽  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Point Boundary ◽  
Coupled Fixed Point Theorem ◽  
Fractional Differential

We study sufficient conditions for existence of solutions to the coupled systems of higher order hybrid fractional differential equations with three-point boundary conditions. For this motive, we apply the coupled fixed point theorem of Krasnoselskii type to form adequate conditions for existence of solutions to the proposed system. We finish the paper with suitable illustrative example.

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

scholarly journals Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Mujahid Abbas ◽  
Bashir Ali ◽  
Yusuf I. Suleiman
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Common Solution ◽  
Contractive Mappings ◽  
Multiplicative Metric Spaces

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.

scholarly journals Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2009
Author(s):  
Badshah-e-Rome ◽  
Muhammad Sarwar ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Of Solutions

In this article, the concept of extended fuzzy rectangular b-metric space (EFRbMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFRbMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed.

scholarly journals Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Kushal Roy ◽  
Mantu Saha ◽  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Couple Fixed Point ◽  
Contractive Mappings

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.

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