scholarly journals Sehgal–Guseman-Type Fixed Point Theorem in b-Rectangular Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3149
Author(s):  
Dingwei Zheng ◽  
Guofei Ye ◽  
Dawei Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Solution ◽  
Point Theory ◽  
Banach’S Fixed Point Theorem ◽  
Rectangular Metric Space

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space). The result presented in the paper generalizes and unifies some results in fixed point theory.

A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space

2018 ◽  
Vol 68 (5) ◽  
pp. 1113-1116 ◽  
Author(s):  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Solution ◽  
Banach Contraction ◽  
Banach’S Fixed Point Theorem ◽  
Rectangular Metric Space

Abstract In this note we give very short proofs for Banach contraction principle theorem in the b-rectangular metric spaces and b-metric spaces. Our result provides a complete solution to an open problem raised by George, Radenović, Reshma and Shukla.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

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.

Maia-Perov type fixed point results for Presic type operators

2017 ◽  
Vol 33 (3) ◽  
pp. 265-274
Author(s):  
MARGARETA-ELIZA BALAZS ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Basic Problem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fredholm Type ◽  
System Of Integral Equations

Starting from the results, established in [Albu, M., A fixed point theorem of Maia-Perov type. Studia Univ. Babes¸- Bolyai Math., 23 (1978), No. 1, 76–79] and [Mures¸an, V., Basic problem for Maia-Perov’s fixed point theorem, Seminar on Fixed Point Theory, Babes¸ Bolyai Univ., Cluj-Napoca, (1988), Preprint Nr. 3, pp. 43–48] where fixed point theorems of Maia-Perov type are proved, the main aim of this paper is to extend this results to product metric spaces, using Presiˇ c type operators. An existence, uniqueness and data dependence theorem related to the ´ solution of the system of integral equations of Fredholm type in product metric spaces, is also presented.

scholarly journals On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Fixed Point Properties ◽  
Contractive Maps

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

scholarly journals Fixed Point Theorems on Generalized Rectangular Metric Spaces

2021 ◽  
Vol 65 (1) ◽  
pp. 59-84
Author(s):  
O. K. Adewale ◽  
◽  
J. O. Olaleru ◽  
H. Olaoluwa ◽  
H. Akewe
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Rectangular Metric Space

In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.

scholarly journals A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3875-3884 ◽  
Author(s):  
Hamid Baghani ◽  
Maryam Ramezani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Set Valued Mappings

In this paper, firstly, we introduce the notion of R-complete metric spaces. This notion let us to consider fixed point theorem in R-complete instead of complete metric spaces. Secondly, as motivated by the recent work of Amini-Harandi (Fixed Point Theory Appl. 2012, 2012:215), we explain a new generalized contractive condition for set-valued mappings and prove a fixed point theorem in R-complete metric spaces which extends some well-known results in the literature. Finally, some examples are given to support our main theorem and also we find the existence of solution for a first-order ordinary differential equation.

scholarly journals Determination of the Some Results for Coupled Fixed Point Theory in C*-Algebra Valued Metric Spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 258-265
Author(s):  
Saleh Omran ◽  
Özen ÖZER
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Numerical Examples ◽  
C Algebra

In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spaces. We get a C*-algebra valued metric space which get values in noncomutative operators. We demonstrate existance and uniqeness of coupled fixed point in a such space. Besides, we support our results by giving numerical examples.

scholarly journals Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Salman Furqan ◽  
Hüseyin Işık ◽  
Naeem Saleem
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Fixed Point Theorem ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Rectangular Metric Space

In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.

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