Systems of variational relations with lower semicontinuous set-valued mappings

In this paper, we use fixed point techniques to establish existence criteria of the solution for a system of two variational relations with lower semicontinuous set-valued mappings.

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On existence result of a class of nonlinear integral equation

Filomat ◽

10.2298/fil1711593b ◽

2017 ◽

Vol 31 (11) ◽

pp. 3593-3597

Author(s):

Ravindra Bisht

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Existence And Uniqueness ◽

Existence Result ◽

Nonlinear Integral Equation ◽

Continuous Functions ◽

Concave Functions ◽

Real Numbers ◽

Fixed Point Techniques ◽

Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

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Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

Abstract and Applied Analysis ◽

10.1155/2014/580621 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Jinlu Li ◽

Ying Liu ◽

Hongya Gao

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Topological Structure ◽

Fixed Point Theorems ◽

Equilibrium Problems ◽

Saddle Points ◽

Order Relation ◽

Partial Order Relation ◽

Chain Complete ◽

Set Valued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

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Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces

Journal of Fixed Point Theory and Applications ◽

10.1007/s11784-017-0401-9 ◽

2017 ◽

Vol 19 (3) ◽

pp. 2129-2143 ◽

Cited By ~ 8

Author(s):

Lili Chen ◽

Lu Gao ◽

Deyun Chen

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Fixed Point Theorems ◽

Set Valued Mappings

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Fixed point techniques in a cone with applications

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(77)90143-3 ◽

1977 ◽

Vol 61 (1) ◽

pp. 58-71 ◽

Cited By ~ 24

Author(s):

J.A Gatica ◽

Hal L Smith

Keyword(s):

Fixed Point ◽

Fixed Point Techniques

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A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-212188 ◽

2021 ◽

pp. 1-21

Author(s):

Rashwan A. Rashwan ◽

Hasanen A. Hammad ◽

A. Nafea

Keyword(s):

Fixed Point ◽

Contraction Mapping ◽

Metric Spaces ◽

Mixed Monotone Property ◽

Cone Metric Spaces ◽

System Of Integral Equations ◽

Tripled Fixed Point ◽

Fixed Point Techniques ◽

Theoretical Results ◽

Cone Metric

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

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Recent Fixed Point Techniques in Fractional Set-Valued Dynamical Systems

Dynamical Systems - Analytical and Computational Techniques ◽

10.5772/67069 ◽

2017 ◽

Author(s):

Parin Chaipunya ◽

Poom Kumam

Keyword(s):

Fixed Point ◽

Dynamical Systems ◽

Fixed Point Techniques

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F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽

10.3390/math7070586 ◽

2019 ◽

Vol 7 (7) ◽

pp. 586 ◽

Cited By ~ 3

Author(s):

Awais Asif ◽

Muhammad Nazam ◽

Muhammad Arshad ◽

Sang Og Kim

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Common Fixed Point ◽

Functional Equations ◽

Fixed Point Theorems ◽

Metric Spaces ◽

The Third ◽

Set Valued Mappings ◽

Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

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