scholarly journals Kannan type mapping in TVS-valued cone metric spaces and their application to Urysohn integral equations

2013 ◽  
Vol 9 (2) ◽  
pp. 243-255
Author(s):  
Akbar Azam ◽  
Ismat Beg
Keyword(s):  
Integral Equations ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Type Mapping ◽  
Urysohn Integral Equations ◽  
Cone Metric

scholarly journals Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saif Ur Rehman ◽  
Hawraa Akram Yazbek ◽  
Rashad A. R. Bantan ◽  
Mohammed Elgarhy
Keyword(s):  
Integral Equations ◽  
Metric Spaces ◽  
Theoretical Work ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Rational Contraction ◽  
Common Fixed Point Theorems ◽  
Cone Metric ◽  
Unique Common Fixed Point

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

scholarly journals Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Control Function ◽  
Cone Metric Spaces ◽  
Tripled Fixed Point ◽  
Contractive Type ◽  
Theoretical Results ◽  
Cone Metric

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

scholarly journals Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 541
Author(s):  
Shamoona Jabeen ◽  
Zhiming Zheng ◽  
Mutti-Ur Rehman ◽  
Wei Wei ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Continuity Condition ◽  
Graph Structure ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Cone Metric

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.

scholarly journals Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Muhammad Talha Waheed ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Volterra Integral Equations ◽  
Cone Metric Spaces ◽  
Common Solution ◽  
Contractive Type ◽  
Cone Metric

In this paper, we introduce the new concept of coupled fixed-point (FP) results depending on another function in fuzzy cone metric spaces (FCM-spaces) and prove some unique coupled FP theorems under the modified contractive type conditions by using “the triangular property of fuzzy cone metric.” Another function is self-mapping continuous, one-one, and subsequently convergent in FCM-spaces. In support of our results, we present illustrative examples. Moreover, as an application, we ensure the existence of a common solution of the two Volterra integral equations to uplift our work.

scholarly journals Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saif Ur Rehman ◽  
Hassen Aydi
Keyword(s):  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Fredholm Integral Equations ◽  
Cone Metric Spaces ◽  
Common Solution ◽  
Common Fixed Point Theorems ◽  
Cone Metric ◽  
Rational Type

This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .

scholarly journals Some Novel Generalized Strong Coupled Fixed Point Findings in Cone Metric Spaces with Application to Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Saif Ur Rehman ◽  
Sami Ullah Khan ◽  
Abdul Ghaffar ◽  
Shao-Wen Yao ◽  
Mustafa Inc
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Common Solution ◽  
Contractive Type ◽  
Cone Metric ◽  
Type Contraction

Fixed point (FP) has been the heart of several areas of mathematics and other sciences. FP is a beautiful mixture of analysis (pure and applied), topology, and geometry. To construct the link between FP and applied mathematics, this paper will present some generalized strong coupled FP theorems in cone metric spaces. Our consequences give the generalization of “cyclic coupled Kannan-type contraction” given by Choudhury and Maity. We present illustrative examples in support of our results. This new concept will play an important role in the theory of fixed point results and can be generalized for different contractive-type mappings in the context of metric spaces. In addition, we also establish an application in integral equations for the existence of a common solution to support our work.

scholarly journals Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Gui-Xiu Chen ◽  
Shamoona Jabeen ◽  
Saif Ur Rehman ◽  
Ahmed Mostafa Khalil ◽  
Fatima Abbas ◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Point Analysis ◽  
Cone Metric

AbstractIn this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

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