scholarly journals Fixed Point Theorems for Generalized αs-ψ-Contractions with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Zhenhua Ma ◽  
Muhammad Nazam ◽  
Sami Ullah Khan ◽  
Xiangling Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Sufficient Conditions ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Unique Common Fixed Point

We study the sufficient conditions for the existence of a unique common fixed point of generalized αs-ψ-Geraghty contractions in an αs-complete partial b-metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic boundary value problems.

scholarly journals Nonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*

2021 ◽  
pp. 15-26
Author(s):  
Guangchong Yang ◽  
Yanqiu Chen
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonnegative Solutions

Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

scholarly journals Fixed Point Results on Multiplicative Semi-Metric Space

2020 ◽  
Vol 12 (3) ◽  
pp. 341-348
Author(s):  
B. Vijayabaskerreddy ◽  
V. Srinivas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems ◽  
Multiplicative Metric Space ◽  
Unique Common Fixed Point

  In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.

scholarly journals Generalization of common fixed point theorems for weakly commuting maps by altering distances

2000 ◽  
Vol 31 (3) ◽  
pp. 243-250 ◽  
Author(s):  
K. P. R. Sastry ◽  
S. V. R. Naidu ◽  
G. V. R. Babu ◽  
G. A. Naidu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Commuting Maps ◽  
Common Fixed Point Theorems ◽  
Unique Common Fixed Point

The main purpose of this paper is to obtain conditions for the existence of a unique common fixed point for four selfmaps on a complete metric space by altering distances between the points.

scholarly journals Fixed point theorems for weakly beta-admissible pair of F-contractions with application

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Muhammad Nazam ◽  
Nawab Hussain ◽  
Aftab Hussain ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Elliptic Boundary ◽  
Admissible Pair ◽  
Elliptic Boundary Value ◽  
Common Solution ◽  
Set Up ◽  
Common Fixed Point Theorems

In this paper, we introduce a new set Fsb of nonlinear functions. We obtain unique common fixed point theorems for (β; F)-weak contractions under the effect of functions from Fsb. Moreover, we deduce new common fixed point results in ordered and graphic b-metric spaces. Our work generalizes several recent results existing in the literature. We set up an example to elucidate main result. We apply the main theorem to show the existence of common solution of the system of elliptic boundary value problems.

scholarly journals Fixed Point Results for Dualistic Contractions with an Application

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Nazam ◽  
Aiman Mukheimer ◽  
Hassen Aydi ◽  
Muhammad Arshad ◽  
Raheel Riaz
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Comparison Property

In this paper, by introducing a convergence comparison property of a self-mapping, we establish some new fixed point theorems for Bianchini type, Reich type, and Dass-Gupta type dualistic contractions defined on a dualistic partial metric space. Our work generalizes and extends some well known fixed point results in the literature. We also provide examples which show the usefulness of these dualistic contractions. As an application of our findings, we demonstrate the existence of the solution of an elliptic boundary value problem.

scholarly journals Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation

2005 ◽  
Vol 2005 (16) ◽  
pp. 2617-2629 ◽  
Author(s):  
Bijendra Singh ◽  
Shishir Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fuzzy Metric Space ◽  
Topological Spaces ◽  
Implicit Relation ◽  
Fuzzy Metric ◽  
Unique Common Fixed Point

The concept of semicompatibility has been introduced in fuzzy metric space and it has been applied to prove results on existence of unique common fixed point of four self-maps satisfying an implicit relation. Recently, Popa (2002) has employed a similar but not the same implicit relation to obtain a fixed point theorem ford-complete topological spaces. All the results of this paper are new.

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