scholarly journals Suzuki-Edelstein Type Contractions via Auxiliary Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Peyman Salimi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Complete Metric Space ◽  
Existence Results ◽  
Partially Ordered ◽  
Auxiliary Functions ◽  
Type Mapping

We prove the existence and uniqueness of a fixed point of certain type mapping, extension of Suzuki-Edelstein mapping, in a partially ordered complete metric space. Our results extend, improve, and generalize the existence results on the topic in the literature. We state some examples to illustrate our results.

scholarly journals Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-Quasi Contraction Type Mapping in Partially Ordered Metric-Like Spaces

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 74 ◽  
Author(s):  
Haitham Qawaqneh ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Habes Alsamir
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partially Ordered ◽  
Type Mapping ◽  
Admissible Mapping ◽  
Contraction Type ◽  
Common Fixed Point Theorems

The aim of this paper is to establish the existence of some common fixed point results for generalized Geraghty ( α , ψ , ϕ ) -quasi contraction self-mapping in partially ordered metric-like spaces. We display an example and an application to show the superiority of our results. The obtained results progress some well-known fixed (common fixed) point results in the literature. Our main results cannot be specifically attained from the corresponding metric space versions. This paper is scientifically novel because we take Geraghty contraction self-mapping in partially ordered metric-like spaces via α − admissible mapping. This opens the door to other possible fixed (common fixed) point results for non-self-mapping and in other generalizing metric spaces.

scholarly journals Further discussion on modified multivalued α*-ψ-contractive type mapping

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1893-1900 ◽  
Author(s):  
Muhammad Ali ◽  
Tayyab Kamran ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Type Mapping ◽  
Contractive Type

In this paper, we investigate the existence of a fixed point for modified multivalued ?*-?-contractive type mapping in the context of complete metric space. We also construct some examples to illustrate the main result. Our results extend, improve and generalize the results on the topic in the literature.

scholarly journals Fixed point theorems for rational type $F$-contraction

2021 ◽  
Vol 13 (1) ◽  
pp. 39-47
Author(s):  
Ö. Acar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Integral Type ◽  
Type Mapping ◽  
Rational Type

In this paper, we consider rational type $F$-contraction for multivalued integral type mapping on a complete metric space. Using Wardowski’s technique, we establish the existence of a fixed point of the multivalued integral type mapping, if this mapping or the $F$-contraction is continuous. In the end, we give an example which shows that our result is the best.

scholarly journals Nonunique Fixed Point Results via Kannan F -Contraction on Quasi-Partial b -Metric Space

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pragati Gautam ◽  
Santosh Kumar ◽  
Swapnil Verma ◽  
Gauri Gupta
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Type Mapping ◽  
Contractive Type

This paper is aimed at acquainting with a new Kannan F -expanding type mapping by the approach of Wardowski in the complete metric space. We establish some fixed point results for Kannan F -expanding type mapping and F -contractive type mappings which satisfy F -contraction conditions. Additionally, some new results are given which generalize several results present in the literature. Moreover, some applications and examples are provided to show the practicality of our results.

scholarly journals A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3001
Author(s):  
Mi Zhou ◽  
Naeem Saleem ◽  
Xiaolan Liu ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Open Problems ◽  
Fuzzy Metric Spaces ◽  
Auxiliary Functions ◽  
Fuzzy Metric ◽  
Contractivity Condition

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

scholarly journals Some Results on S-Contractions of Type E

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 195
Author(s):  
Andreea Fulga ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Complete Metric Space ◽  
Simulation Functions ◽  
Composite Form

In this manuscript, we consider the compositions of simulation functions and E-contraction in the setting of a complete metric space. We investigate the existence and uniqueness of a fixed point for this composite form. We give some illustrative examples and provide an application.

scholarly journals Generalized fixed point results of rational type contractions in partially ordered metric spaces

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
N. Seshagiri Rao ◽  
K. Kalyani
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type ◽  
Type Contraction

Abstract Objectives We investigated the existence and uniqueness of a fixed point for the mapping satisfying generalized rational type contraction conditions in metric space endowed with partial order. Suitable examples are presented to justify the results obtained. Result Some new fixed point results have been obtained for a mapping fulfilling generalized contractions. The uniqueness of the fixed point is also the part of the study based on an ordered relation. One example is given for a result which is not valid in the usual metric space.

scholarly journals COUPLED FIXED POINT THEOREMS WITH C-CLASS FUNCTIONS

2018 ◽  
pp. 109
Author(s):  
Arslan H. Ansari ◽  
Murat Ozdemir ◽  
Mohammad S. Khan ◽  
Isa Yildirim
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Partially Ordered ◽  
New Type

In this paper, we introduce a new type of coupled …xed point theoremwith C-class functions in partially ordered complete metric space.

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