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Items from 1 to 20 out of 600 results

article

Banach, Kannan, Chatterjea, and Reich‐type contractive inequalities for multivalued mappings and their common fixed points

Pradip Debnath

Mathematical Methods in the Applied Sciences > 45 > 3 > 1587 - 1596

In this paper, we present Banach, Kannan, Chatterjea, and Reich‐type contractive inequalities for multivalued mappings and prove the existence of their common fixed points in a complete metric space without assuming compactness of the images under those mappings.

article

Solving system of linear equations via bicomplex valued metric space

Arul Joseph Gnanaprakasam, Salah Mahmoud Boulaaras, Gunaseelan Mani, Bahri Cherif, more

Demonstratio Mathematica > 2021 > Vol. 54, nr 1 > 474--487

In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

article

Common best proximity points for proximally F–dominated mappings

Rakesh Batra

Fasciculi Mathematici > 2020 > nr 63 > 23--37

The principal aim of this work is to formulate an extension and improvement of the common best proximity point theorem for a pair of non-self mappings, one of which is dominated by the other as proved by Basha. The proposed extension discusses a common best proximity point theorem for a pair of non-self mappings, one of which is F-dominated by the other proximally, for a function F as defined by Wardowski.

article

Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

Phatiphat Thounthong, Nuttapol Pakkaranang, Phachara Saipara, Pawicha Phairatchatniyom, more

Mathematical Methods in the Applied Sciences > 42 > 17 > 5929 - 5943

The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ‐convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non‐trivial examples are also provided to show performance and comparison speed of convergence with many previously known...

article

Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations

Jian-Zhong Xiao, Yue Zhu

Computational and Applied Mathematics > 2019 > 38 > 4 > 1-11

In this paper a modified Ishikawa iterative process for approximating a common fixed point of a locally asymptotically nonexpansive cosine family is firstly introduced, and then, by using the theory of cosine families and constructing some control conditions, several strong convergence theorems are established for this iterative process in Banach spaces. Moreover, an example is presented to illustrate...

article

Approximate coincidence point and common fixed point results for a hybrid pair of mappings with constraints in partially ordered Menger PM-spaces

Zhaoqi Wu, Mengdi Liu, Chuanxi Zhu, Chunfang Chen

Journal of Inequalities and Applications > 2019 > 2019 > 1 > 1-14

We study an approximate coincidence point and a common fixed point problem for a hybrid pair of mappings with constraints in Menger PM-spaces, and obtain some new results. We derive interesting consequences of the main results by using the properties of a Menger–Hausdorff metric, and analogous results based on graphs instead of partial orders can be similarly formulated. Moreover, we construct two...

article

Relation-theoretic coincidence and common fixed point results under (F,R)g $(F,\mathcal{R})_{g}$-contractions with an application

Waleed M. Alfaqih, Mohammad Imdad, Rqeeb Gubran, Idrees A. Khan

Fixed Point Theory and Applications > 2019 > 2019 > 1 > 1-18

In this paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of (F,R)g $(F,\mathcal{R})_{g}$-contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting...

article

Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces

Jafar Bakhande, Shahram Saeidi

Journal of Fixed Point Theory and Applications > 2019 > 21 > 3 > 1-12

In this paper, we will be concerned with a problem raised by Lau (Fixed Point Theory Appl, 2010) for the existence of common fixed points for a right reversible semitopological semigroup S acting asymptotically nonexpansive on a nonempty compact convex set in the framework of locally convex spaces. We give answers to this problem under the left amenability of $$\text {ARUC}(S)$$ ARUC(S) and $$\text...

article

Common fixed point results for class of set-contraction mappings endowed with a directed graph

Abdul Latif, Talat Nazir, Marwan Amin Kutbi

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 4 > 3207-3222

We present common fixed point results of finite family of set-valued mappings satisfying generalized graphic contractions on set-valued domain endowed with a directed graph. Some examples are presented to support the results proved therein. Consequently, our results unify, improve and generalize various comparable known results.

article

Common solution to a pair of non-linear matrix equations via fixed point results

Hiranmoy Garai, Lakshmi Kanta Dey

Journal of Fixed Point Theory and Applications > 2019 > 21 > 2 > 1-18

In this paper, we propose an idea to derive some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed with this, we present some interesting common fixed point results involving a couple of altering distance functions along with another control function in Banach spaces. Based on these results, we deduce...

article

Convergence analysis for a new two-step iteration process for G-nonexpansive mappings with directed graphs

Tanakit Thianwan, Damrongsak Yambangwai

Journal of Fixed Point Theory and Applications > 2019 > 21 > 2 > 1-16

In this paper, we introduce and study convergence analysis of a new two-step iteration process when applied to class of G-nonexpansive mappings. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space with a directed graph. Moreover, weak convergence theorem without making use of the Opial’s condition is proved. We also show the...

article

Approximation of common fixed points of strongly nonexpansive sequences in a Banach space

Koji Aoyama, Masashi Toyoda

Journal of Fixed Point Theory and Applications > 2019 > 21 > 1 > 1-16

The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.

article

An inertial S-iteration process

Aniruth Phon-on, Nifatamah Makaje, Areeyuth Sama-Ae, Kittiya Khongraphan

Fixed Point Theory and Applications > 2019 > 2019 > 1 > 1-14

In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speeding up the convergence of the algorithm. We then prove the convergence theorems of a sequence generated by our new method for finding a common fixed point of nonexpansive mappings in a Banach space...

article

Existence and convergence theorems for Berinde nonexpansive multivalued mapping on Banach spaces

Nuttawut Bunlue, Suthep Suantai

Afrika Matematika > 2019 > 30 > 3-4 > 483-494

In this paper, we first prove existence of fixed points for Berinde nonexpansive multivalued mappings on Banach spaces. Moreover, we obtain convergence theorems for common fixed point of Berinde and quasi-nonexpansive mappings. The main results obtained in this paper extened and generalize some of the well-known results in the literature.

article

Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

M. Sarwar, H. Humaira, H. Huang

Commentationes Mathematicae > 2018 > Vol. 58, No. 1/2 > 57--78

In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.

article

Some results on implicit contractive conditions in metric spaces endowed with arbitrary binary relations

Nantaporn Chuensupantharat, Poom Kumam

Mathematical Methods in the Applied Sciences > 41 > 17 > 7384 - 7398

The main purpose of this study is to establish some coincidence and common fixed point theorems for 2 self‐mappings via the condition of implicit function on metric spaces provided with arbitrary binary relation. In our results, the main theorems are the generalized version of the literatures, and we also give some examples to guarantee our main results. Moreover, we show that the result to guarantee...

article

Common Fixed Points of Continuous Mappings on S-Metric Spaces

N. Taş, N. Yılmaz Özgür

Mathematical Notes > 2018 > 104 > 3-4 > 587-600

The aim of this paper is to obtain some common fixed point results on an S-metric space. For this purpose, we prove new generalized common fixed point theorems using the notions of weak commutation, compatibility, and orbital continuity for two and four continuous self-mappings. Our main results generalize the known common fixed point theorems on metric spaces.

article

Common fixed point theorems for set-valued mappings in normed spaces

Mircea Balaj, Mohamed A. Khamsi

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 3 > 1893-1905

Let $$\Phi $$ Φ be the class of all real functions $$\varphi : [0, \infty [ \times [0, \infty [ \rightarrow [0, \infty [$$ φ : [ 0 , ∞ [ × [ 0 , ∞ [ → [ 0 , ∞ [ that satisfy the following condition: there exists $$\alpha \in ]0, 1[ \text { such that } \varphi ((1 - \alpha ) r, \alpha r) < r,\; \text { for all } r > 0$$ α ∈ ] 0 , 1 [ such that φ ( ( 1 - α ) r , α r ) <...

article

Some generalizations of fixed point theorems and common fixed point theorems

Jang Hyun Jo

Journal of Fixed Point Theory and Applications > 2018 > 20 > 4 > 1-17

We present some fixed point theorems and common fixed point theorems which generalize and unify previous known results.

article

Simulation functions: a survey of recent results

Ankush Chanda, Lakshmi Kanta Dey, Stojan Radenović

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2019 > 113 > 3 > 2923-2957

This article surveys many of the recent works regarding simulation functions and $$\mathcal {Z}$$ Z -contractions that came into existence after the publication of Khojasteh et al. (Filomat 29(6):1189–1194, 2015). These results assess inclusive of simulation functions, $$\mathcal {Z}$$ Z -contractions, b-simulation functions, Suzuki-type $$\mathcal {Z}$$ Z -contractions, Darbo’s fixed...

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Banach, Kannan, Chatterjea, and Reich‐type contractive inequalities for multivalued mappings and their common fixed points

Solving system of linear equations via bicomplex valued metric space

Common best proximity points for proximally F–dominated mappings

Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations

Approximate coincidence point and common fixed point results for a hybrid pair of mappings with constraints in partially ordered Menger PM-spaces

Relation-theoretic coincidence and common fixed point results under (F,R)g $(F,\mathcal{R})_{g}$-contractions with an application

Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces

Common fixed point results for class of set-contraction mappings endowed with a directed graph

Common solution to a pair of non-linear matrix equations via fixed point results

Convergence analysis for a new two-step iteration process for G-nonexpansive mappings with directed graphs

Approximation of common fixed points of strongly nonexpansive sequences in a Banach space

An inertial S-iteration process

Existence and convergence theorems for Berinde nonexpansive multivalued mapping on Banach spaces

Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces

Some results on implicit contractive conditions in metric spaces endowed with arbitrary binary relations

Common Fixed Points of Continuous Mappings on S-Metric Spaces

Common fixed point theorems for set-valued mappings in normed spaces

Some generalizations of fixed point theorems and common fixed point theorems

Simulation functions: a survey of recent results

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