scholarly journals Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 894
Author(s):  
Murchana Neog ◽  
Mohammed M. M. Jaradat ◽  
Pradip Debnath
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
Weak Contraction ◽  
Life Problems ◽  
Ulam Theorem ◽  
The Given ◽  
Point Argument

The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

scholarly journals PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1375 ◽  
Author(s):  
Mohammed M. M. Jaradat ◽  
Babak Mohammadi ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Zead Mustafa
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
Control Engineering ◽  
Life Problems ◽  
Ulam Theorem ◽  
Delay Differential ◽  
And Control

The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ − F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

scholarly journals Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mappings ◽  
New Type ◽  
The Given ◽  
Kannan Contraction

In this paper, we use interpolation to obtain fixedpoint and common fixed point results for a new type of Kannan contraction mappings in complete metric and b -metric spaces. Our results extend and improve some results on fixed point theory in the literature. We also give some examples to illustrate the given results.

Probabilistic contraction under a control function

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Binayak S. Choudhury ◽  
Vandana Tiwari ◽  
Tanmoy Som ◽  
Parbati Saha
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Control Function ◽  
Real Life ◽  
Point Theory ◽  
Probabilistic Metric Spaces ◽  
Control Functions ◽  
Life Problems ◽  
Probabilistic Metric

Abstract Probabilistic metric spaces are metric structures having uncertainty built within their geometry, which has made them into an appropriate context for modelling many real life problems. Theoretical studies on these structures have also appeared extensively. This paper is intended for some development of fixed point theory in probabilistic metric spaces, which is an active area of contemporary research. We define a new contraction mapping in such spaces and show that the contraction has a unique fixed point if such spaces are G-complete with an arbitrary choice of a continuous t-norm. With a minimum t-norm, the result is further extended in any complete probabilistic metric space. The contraction is defined with the help of a control function which is different from several other control functions used in probabilistic fixed point theory by other authors. The methodology of the proof is new. An illustrative example is given. The present work is a part of probabilistic analysis.

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

scholarly journals A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 512 ◽  
Author(s):  
Erdal Karapınar ◽  
Panda Kumari ◽  
Durdana Lateef
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nash Equilibria ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
New Approach ◽  
Correctness Of Programs

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

scholarly journals Common Fixed Point Theorems for Generalized Cyclic Contraction Pair in Partial B-Metric Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 85-89
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of generalized cyclic contraction pair with transitive mapping in partial b-metric spaces. Also, we establish some fixed point theorems for this contraction pair. Our results generalize and improve the result of Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho (Fixed Point Theory App. 2015:164) in partial-b-metric spaces.

scholarly journals Common fixed point theorem for four mappings satisfying generalized weak contractive condition

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 1-10 ◽  
Author(s):  
Mujahid Abbas ◽  
Dragan Djoric
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Applied Mathematics ◽  
Point Theory ◽  
Contractive Condition ◽  
Mathematics Subject Classifications ◽  
Common Fixed Point Theorem

Contractive conditions introduced in (Q. Zhang and Y. Song, Fixed point theory for generalized ?-weak contraction, Appl. Math. Lett. 22(2009), 75-78) and (D. Djoric, Common fixed point for generalized (?, ?)-weak contractions, Applied Mathematics Letters, 22(2009), 1896-1900) are employed to obtain a new common fixed point theorem for four maps. Our result substantially generalizes comparable results in the literature. 2010 Mathematics Subject Classifications. 47H10. .

scholarly journals Common Fixed Point Results for Rational (α,β)φ-mω Contractions in Complete Quasi Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 392 ◽  
Author(s):  
Tariq Qawasmeh ◽  
Wasfi Shatanawi ◽  
Anwar Bataihah ◽  
Abdalla Tallafha
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Distance Mapping

The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

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