scholarly journals Cyclic Mappings and Further Results in B-Metric-Like Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shengquan Weng ◽  
Quanxin Zhu ◽  
Baoying Du ◽  
Kaibo Shi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Formula Type

Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.

scholarly journals Pseudo Picard operators on generalized metric spaces

2018 ◽  
Vol 12 (2) ◽  
pp. 389-400 ◽  
Author(s):  
Ishak Altun ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Generalized Metric

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. Jleli and B. Samet: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.

A fixed point problem with constraint inequalities via a contraction in incomplete metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3365-3379 ◽  
Author(s):  
Z. Ahmadi ◽  
R. Lashkaripour ◽  
H. Baghani
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Complete Metric Spaces ◽  
New Class ◽  
Constraint Inequalities ◽  
Weaker Conditions

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

A new contribution to the fixed point theory in b-generalized metric spaces

2017 ◽  
Vol 8 (1) ◽  
pp. 111
Author(s):  
Ahmed H. Soliman ◽  
M. A. Ahmed ◽  
A. M. Zidan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Rational Type

In this work, we introduce a new generalized metric space called b-generalized metric spaces (shortly, b-G.M.S). Also, we establish some fixed point results for a contraction of rational type in b-G.M.S. Some interesting examples are also given.

scholarly journals Common Fixed Point for Two Pairs of Mappings Satisfying (E.A) Property in Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Wei Long ◽  
Mujahid Abbas ◽  
Talat Nazir ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Common Fixed Point Problem

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem.

scholarly journals Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Choonkil Park ◽  
Manuel de la Sen ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Work ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
New Type ◽  
Uniqueness And Existence

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U -contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equations.

scholarly journals Conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory

2021 ◽  
Vol 37 (2) ◽  
pp. 345-354
Author(s):  
ALEXANDRU-DARIUS FILIP
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest Timişoara, Mat.-Inform., 46 (2008), 149–160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101–110). We start our considerations with an overview of generalized metric spaces with \mathbb{R}_+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered.

On the theory of fixed point theorems for convex contraction mappings

2015 ◽  
Vol 31 (3) ◽  
pp. 365-371
Author(s):  
VIORICA MURESAN ◽  
◽  
ANTON S. MURESAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Shadowing Property ◽  
Contraction Mappings ◽  
Limit Shadowing

Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

scholarly journals On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Abdullah Alotaibi
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Monotone Mapping ◽  
Coupled Fixed Point ◽  
Active Role ◽  
Generalized Metric Space ◽  
Generalized Metric

Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup.

scholarly journals A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
C. Izuchukwu ◽  
F. O. Isiogugu ◽  
C. C. Okeke
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Iteration Process ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Point Problem ◽  
Common Solution

Abstract In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.

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