Some common best proximity point theorems via a fixed point theorem in metric spaces

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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Chatterjea-type fixed point theorem on cone rectangular metric spaces with banach algebras

10.1063/5.0040595 ◽

2021 ◽

Author(s):

Abba Auwalu ◽

Ali Denker

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Spaces ◽

Banach Algebras

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Fixed-point theorem for asymptotic contractions of Meir–Keeler type in complete metric spaces

Nonlinear Analysis ◽

10.1016/j.na.2005.04.054 ◽

2006 ◽

Vol 64 (5) ◽

pp. 971-978 ◽

Cited By ~ 38

Author(s):

Tomonari Suzuki

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Spaces ◽

Complete Metric Spaces

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Semicompatibility and fixed point theorems in an unboundedD-metric space

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.789 ◽

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.

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Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

Creative Mathematics and Informatics ◽

10.37193/cmi.2018.01.06 ◽

2018 ◽

Vol 27 (1) ◽

pp. 37-48

Author(s):

ANDREI HORVAT-MARC ◽

◽

LASZLO BALOG ◽

Keyword(s):

Boundary Condition ◽

Fixed Point ◽

Fixed Point Theorem ◽

Banach Spaces ◽

Point Theorem ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

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

Symmetry ◽

10.3390/sym10100512 ◽

2018 ◽

Vol 10 (10) ◽

pp. 512 ◽

Cited By ~ 13

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.

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