scholarly journals Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions

2021 ◽  
Vol 7 (1) ◽  
pp. 315-333
Author(s):  
Maysaa Al-Qurashi ◽  
◽  
Mohammed Shehu Shagari ◽  
Saima Rashid ◽  
Y. S. Hamed ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Intuitionistic Fuzzy Set ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Fixed Point ◽  
Functional Inclusion

<abstract><p>In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.</p></abstract>

scholarly journals Fixed Point Results in Orthogonal Neutrosophic Metric Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Umar Ishtiaq ◽  
Khalil Javed ◽  
Fahim Uddin ◽  
Manuel de la Sen ◽  
Khalil Ahmed ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Space ◽  
Metric Spaces ◽  
Intuitionistic Fuzzy Set ◽  
Neutrosophic Set ◽  
Imprecise Data ◽  
Intuitionistic Fuzzy ◽  
Neutrosophic Logic ◽  
The Relationship

Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metric space. Some fixed point results are investigated in this setting. For the validity of the obtained results, some nontrivial examples are given.

A fuzzy fixed point problem for constraint inequalities

2020 ◽  
Vol 39 (3) ◽  
pp. 3025-3032
Author(s):  
Hüseyin Işık ◽  
Muzeyyen Sangurlu Sezen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
New Approach ◽  
Fuzzy Metric ◽  
Constraint Inequalities ◽  
Fuzzy Fixed Point

In this work, we prove a new fixed point theorem in the setting fuzzy metric spaces. The fuzzy metric space considered here is assumed to have two partial orders defined on it. We introduce a new approach to the existence of a fixed point of a function satisfying the two constraint inequalities. An example is included which illustrates new results of this paper. Moreover, an application of our result to the study of integral equations is provided.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
R. K. Sharma ◽  
Sumit Chandok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Contraction Mappings ◽  
Integro Differential Equation

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ -contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam’s stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals A fixed point result for multivalued generalized contraction maps

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 929-933 ◽  
Author(s):  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Generalized Contraction ◽  
Fixed Point Result ◽  
Contraction Maps

Using the concept of u-distance, a fixed point problem in metric spaces for closed valued maps, is solved. Consequently, several known fixed point results are either improved or generalized.

scholarly journals Some Fixed-Point Results via Mix-Type Contractive Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Özlem Acar
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Rational Type ◽  
Type Contraction

We consider a fixed-point problem for mappings involving a rational type and almost type contraction on complete metric spaces. To do this, we are using F -contraction and H , φ -contraction. We also present an example to illustrate our result.

scholarly journals On Ćirić-Prešić Operators in Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Narongsuk Boonsri ◽  
Satit Saejung ◽  
Kittipong Sitthikul
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Classical Approach ◽  
Single Variable ◽  
Several Variables ◽  
Convergence Problems

We show that the Prešić type operators of several variables can be regarded as an operator of a single variable and the fixed point problem of Prešić type can be regarded as a classical fixed point problem. We extend the recent result of Ćirić and Prešić by using the classical approach of Prešić. The key of the proof is based on the mappings introduced by Kada, Suzuki, and Takahashi. We also discuss the convergence problems of recursive real sequences and the Volterra integral equations as an application of our result.

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