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.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

2021 ◽  
pp. 1-21
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
A. Nafea
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Mixed Monotone Property ◽  
Cone Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Fixed Point Techniques ◽  
Theoretical Results ◽  
Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

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 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 NEW FIXED POINT RESULTS FOR T-CONTRACTIVE MAPPING WITH c-DISTANCE IN CONE METRIC SPACES

2020 ◽  
pp. 367
Author(s):  
Anil Kumar Dubey ◽  
Urmila Mishra ◽  
Nirmal Kumar Singh ◽  
Mithilesh Deo Pandey
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Cone Metric Spaces ◽  
Type Mapping ◽  
Contractive Type ◽  
Cone Metric

In this article, we generalize and improve the results of Fadail et al.[Z. M. Fadail and S. M. Abusalim, Int. Jour. of Math. Anal., Vol. 11, No. 8(2017), pp. 397-405.] and Dubey et al.[AnilKumar Dubey and Urmila Mishra, Non. Func. Anal. Appl., Vol. 22, No. 2(2017), pp 275-286.] under the concept of a c-distance in cone metric spaces. We prove the existence and uniqueness of the fixed point for T -contractive type mapping under the concept of c-distance in cone metric spaces.

scholarly journals Fixed Point Results for F-Contractions in Cone Metric Spaces over Topological Modules and Applications to Integral Equations

2021 ◽  
Vol 6 (1) ◽  
pp. 16
Author(s):  
Adrian Nicolae Branga
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Fractional Integral Equation ◽  
Topological Modules ◽  
Cone Metric

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integral equations were presented in the last part of the article, one of them being a fractional integral equation.

Solving a system of integral equations by using some tripled fixed point theorems

2020 ◽  
Vol 29 (1) ◽  
pp. 51-56
Author(s):  
MONICA LAURAN ◽  
ADINA POP
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Uniqueness Of A Solution ◽  
Theoretical Results

A tripled fixed point theorems in ordered metric spaces is used in order to prove the existence and uniqueness of a solution for a class of integral equations. The conditions of the theorem are much weaker than those existing in literature and the theorem is useful for solving some general problems. An example to illustrate our theoretical results is also given.

scholarly journals On Complete Cone Metric Space and Fixed Point Theorem

2011 ◽  
Vol 3 (2) ◽  
pp. 303-309
Author(s):  
J. Mehta ◽  
M. L. Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weakly Compatible Maps ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Contractive Type ◽  
Cone Metric

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.Keywords: Common fixed point; Complete cone metric space; Weakly compatible maps.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6475                J. Sci. Res. 3 (2), 303-309 (2011)

scholarly journals Fixed Point Results for Weakφ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Biwen Li ◽  
Huaping Huang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Uniqueness Of A Solution ◽  
Cone Metric

By using a nontrivial proof method, the purpose of this paper is to obtain some fixed point results for weakφ-contractions in cone metric spaces over Banach algebras. Several examples and applications to the existence and uniqueness of a solution to two classes of equations are also given.

scholarly journals BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES

2021 ◽  
pp. 1239
Author(s):  
Zeinab Eivazi Damirchi Darsi Olia ◽  
Madjid Eshaghi Gordji ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Banach Fixed Point Theorem ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

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