scholarly journals New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Weng-Seng Heng ◽  
Wei-Shih Du ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Convexity Property ◽  
Linear Spaces ◽  
Compact Metric Spaces

We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

scholarly journals SOME FIXED POINT THEOREMS VIA CYCLIC CONTRACTIVE CONDITIONS IN S-METRIC SPACES

2021 ◽  
pp. 377
Author(s):  
Gurucharan Singh Saluja
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posed

We present some fixed point theorems for mappings which satisfy certain cyclic contractive conditions in the setting of $S$-metric spaces. The results presented in this paper generalize or improve many existing fixed point theorems in the literature. We also presented an application of our result to well-posed of fixed point problem. To support our results, we give some examples.

scholarly journals The ordered implicit relations and related fixed point problems in the cone $ b $-metric spaces

2022 ◽  
Vol 7 (4) ◽  
pp. 5199-5219
Author(s):  
Anam Arif ◽  
◽  
Muhammad Nazam ◽  
Aftab Hussain ◽  
Mujahid Abbas ◽  
...  
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Implicit Relation

<abstract><p>In this paper, we introduce an ordered implicit relation. We present some examples for the illustration of the ordered implicit relation. We investigate conditions for the existence of the fixed points of an implicit contraction. We obtain some fixed point theorems in the cone $ b $-metric spaces and hence answer a fixed-point problem. We present several examples and consequences to explain the obtained theorems. We solve an homotopy problem and show existence of solution to a Urysohn Integral Equation as applications of the obtained fixed point theorem.</p></abstract>

scholarly journals Existence and Uniqueness of Zeros for Vector-Valued Functions with K-Adjustability Convexity and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 809
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Uniqueness Theorems ◽  
New Concepts ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, we introduce the new concepts of K-adjustability convexity and strictly K-adjustability convexity which respectively generalize and extend the concepts of K-convexity and strictly K-convexity. We establish some new existence and uniqueness theorems of zeros for vector-valued functions with K-adjustability convexity. As their applications, we obtain existence theorems for the minimization problem and fixed point problem which are original and quite different from the known results in the existing literature.

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.

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

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 Related fixed point theorems on two complete and compact metric spaces

1998 ◽  
Vol 21 (3) ◽  
pp. 559-563
Author(s):  
R. K. Namdeo ◽  
N. K. Tiwari ◽  
B. Fisher ◽  
Kenan Taş
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces

A new related fixed point theorem on two complete metric spaces is obtained. A generalization is given for two compact metric spaces.

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