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 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.

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 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 The Meir–Keeler Fixed Point Theorem for Quasi-Metric Spaces and Some Consequences

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 741 ◽  
Author(s):  
Salvador Romaguera ◽  
Pedro Tirado
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Nonlinear Difference Equations ◽  
Recurrence Equations

We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a question recently raised in the paper “On the fixed point theory in bicomplete quasi-metric spaces”, J. Nonlinear Sci. Appl. 2016, 9, 5245–5251. We also give an application to the study of existence of solution for a type of recurrence equations associated to certain nonlinear difference equations.

Comments on some fixed point theorems in metric spaces

2018 ◽  
Vol 27 (1) ◽  
pp. 15-20
Author(s):  
VASILE BERINDE ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mapping Principle ◽  
Contraction Condition

In a recent paper [Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), No. 2, 299–305], the author stated and proved a fixed point theorem that is intended to generalize the well known Banach’s contraction mapping principle. In this note we show that the main result in the above paper does not hold at least in two extremal cases for the parameter ε involved in the contraction condition used there. We also present some illustrative examples and related results.

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.

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 Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

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