TRIPLED COINCIDENCE AND COMMON TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS SATISFYING NEW CONTRACTIVE CONDITION

The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Presiˇ c-Kannan type contractive condition: ... or a Presiˇ c-Chatterjea type contractive condition: ... The obtained tripled fixed point theorems extend and unify several related results in literature.

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TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS UNDER GENERALIZED NONLINEAR CONTRACTION

The Pure and Applied Mathematics ◽

10.7468/jksmeb.2014.21.1.23 ◽

2014 ◽

Vol 21 (1) ◽

pp. 23-38 ◽

Cited By ~ 1

Author(s):

Bhavana Deshpande ◽

Sushil Sharma ◽

Amrish Handa

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Tripled Fixed Point ◽

Nonlinear Contraction ◽

Hybrid Pair

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A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽

10.2298/fil1711295n ◽

2017 ◽

Vol 31 (11) ◽

pp. 3295-3305 ◽

Cited By ~ 3

Author(s):

Antonella Nastasi ◽

Pasquale Vetro

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Contractive Condition ◽

Complete Metric Spaces ◽

New Class ◽

Banach Contraction ◽

The Banach Contraction Principle

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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A Generalization of Ćirić Quasicontractions

Abstract and Applied Analysis ◽

10.1155/2012/518734 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 6

Author(s):

Erdal Karapınar ◽

Kieu Phuong Chi ◽

Tran Duc Thanh

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Contractive Condition

We proved a fixed point theorem for a class of maps that satisfy Ćirić's contractive condition dependent on another function. We presented an example to show that our result is a real generalization.

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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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