Some new fixed point results for convex contractions in B-metric spaces

We establish certain fixed point results forα-η-generalized convex contractions,α-η-weakly Zamfirescu mappings, andα-η-Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

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Some New Observations and Results for Convex Contractions of Istratescu’s Type

Symmetry ◽

10.3390/sym11121457 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1457 ◽

Cited By ~ 2

Author(s):

Z. D. Mitrović ◽

H. Aydi ◽

N. Mlaiki ◽

M. Gardašević-Filipović ◽

K. Kukić ◽

...

Keyword(s):

Fixed Point ◽

Contraction Mapping ◽

Metric Spaces ◽

Unique Fixed Point ◽

Convex Contractions

The purpose is to ensure that a continuous convex contraction mapping of order two in b-metric spaces has a unique fixed point. Moreover, this result is generalized for convex contractions of order n in b-metric spaces and also in almost and quasi b-metric spaces.

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Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Annals of West University of Timisoara - Mathematics and Computer Science ◽

10.1515/awutm-2017-0018 ◽

2017 ◽

Vol 55 (2) ◽

pp. 119-142

Author(s):

Flavian Georgescu

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Space ◽

Existence And Uniqueness ◽

Metric Spaces ◽

Iterated Function Systems ◽

Iterated Function ◽

Convex Contractions

AbstractThe concept of generalized convex contraction was introduced and studied by V. Istrăţescu and the notion ofb-metric space was introduced by I. A. Bakhtin and S. Czerwik. In this paper we combine these two elements by studying iterated function systems consisting of generalized convex contractions on the framework ofb-metric spaces. More precisely we prove the existence and uniqueness of the attractor of such a system providing in this way a generalization of Istrăţescu’s convex contractions fixed point theorem in the setting of complete strongb-metric spaces.

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Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2017.1.2 ◽

2016 ◽

Vol 2017 (1) ◽

pp. 17-30 ◽

Cited By ~ 22

Author(s):

Muhammad Usman Ali ◽

◽

Tayyab Kamran ◽

Mihai Postolache ◽

◽

...

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Metric Spaces ◽

Integral Inclusion

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Common Fixed Point Results for Three Maps in Cone Metric Spaces

SOP Transactions on Applied Mathematics ◽

10.15764/am.2014.03005 ◽

2014 ◽

Vol 1 (3) ◽

pp. 42-47

Author(s):

K. Prudhvi ◽

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Metric Spaces ◽

Cone Metric Spaces ◽

Cone Metric

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Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

International Journal of Emerging Research in Management and Technology ◽

10.23956/ijermt.v6i8.155 ◽

2018 ◽

Vol 6 (8) ◽

pp. 297

Author(s):

Jagdish C. Chaudhary ◽

Shailesh T. Patel

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Complete Metric Space ◽

Contractive Condition ◽

Integral Type ◽

Complete Metric Spaces ◽

Common Fixed Point Theorems ◽

Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral type.

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