scholarly journals Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications to Fixed Point Theory

Mathematics ◽  
2018 ◽  
Vol 6 (7) ◽  
pp. 117 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Zhenhua He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

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 Common Fixed Point Theorems for Generalized Cyclic Contraction Pair in Partial B-Metric Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 85-89
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of generalized cyclic contraction pair with transitive mapping in partial b-metric spaces. Also, we establish some fixed point theorems for this contraction pair. Our results generalize and improve the result of Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho (Fixed Point Theory App. 2015:164) in partial-b-metric spaces.

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 Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

scholarly journals Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory Appl. 2011, 2011:93

2012 ◽  
Vol 2012 (1) ◽  
pp. 103 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contraction Mappings ◽  
Modular Metric Spaces

scholarly journals Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

scholarly journals Fixed Point Theory inα-Complete Metric Spaces with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
N. Hussain ◽  
M. A. Kutbi ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
New Concepts ◽  
Rational Contraction

The aim of this paper is to introduce new concepts ofα-η-complete metric space andα-η-continuous function and establish fixed point results for modifiedα-η-ψ-rational contraction mappings inα-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems forψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

scholarly journals Meir-Keeler Contraction In Rectangular M−Metric Space

2021 ◽  
Vol 9 (1) ◽  
pp. 96-104
Author(s):  
Mohammad Asim ◽  
Samad Mujahid ◽  
Izhar Uddin
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Type Contraction

Abstract In this paper, we prove some fixed point theorems for a Meir-Keeler type Contraction in rectangular M−metric space. Thus, our results extend and improve very recent results in fixed point theory.

scholarly journals A unified common fixed point theorem for a family of mappings

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 759-769
Author(s):  
Vijay Dalakoti ◽  
Ravindra Bisht ◽  
R.P. Pant ◽  
Mahesh Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Minimal Set ◽  
Contractive Type ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

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