scholarly journals Fixed point results for weak contractions in partially ordered b-metric space

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
N. Seshagiri Rao ◽  
K. Kalyani ◽  
K. Prasad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contraction Condition ◽  
Generalized Weak Contraction ◽  
Coupled Coincidence

Abstract Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

scholarly journals Some fixed point results of generalized $$(\phi , \psi )$$-contractive mappings in ordered b-metric spaces

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Belay Mitiku ◽  
Kalyani Karusala ◽  
Seshagiri Rao Namana
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Common Fixed Points ◽  
Coupled Coincidence Point ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract Objectives The aim of this paper is to establish some fixed point, coincidence point and, coupled coincidence and coupled common fixed point results for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in partially ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify our results. Result The existence and uniqueness theorems for a fixed point and coincidence point, coupled coincidence point and coupled common fixed points for two mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.

scholarly journals Two theorems in general metric space with 𝛒-distance

2017 ◽  
Vol 12 (12) ◽  
pp. 6852-6862
Author(s):  
Salwa Salman Abed ◽  
Hiba Adel Jabbar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Contraction Condition ◽  
Coupled Coincidence

In this paper, we prove two theorems about fixed point and coupled coincidence point in generalized -metric space via ρ-distance for a mapping satisfying a contraction condition.

scholarly journals Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapınar ◽  
İnci M. Erhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Coupled Coincidence

We prove coupled coincidence point and coupled fixed point results of and involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.

scholarly journals Coupled coincidence point result in partially ordered generalized metric spaces

2012 ◽  
Vol 43 (4) ◽  
pp. 609-619 ◽  
Author(s):  
Vizender Sihag ◽  
Ramesh Kumar Vats
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Computer Modelling ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Generalized Metric Spaces ◽  
Partially Ordered ◽  
Generalized Metric ◽  
Coupled Coincidence

The present study introduces the notion of compatibility in partially ordered G-metric spaces and uses this perception to establish a coupled coincidence point result. Our effort extend the recent work of Choudhary and Maity [B. S. Choudhary, P. Maity, Coupled fixed point results in generalized metric spaces, Mathematical and Computer Modelling 54 (2011) 73-79]. The example demonstrates that our main result is an actual improvement over the results which are generalized

scholarly journals Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Liang ◽  
Chuanxi Zhu ◽  
Zhaoqi Wu ◽  
Chunfang Chen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Coupled Fixed Point ◽  
Coupled Coincidence Point ◽  
Nonlinear Integral Equations ◽  
Partially Ordered ◽  
Coupled Coincidence

Some new coupled coincidence point and coupled fixed point theorems are established in partially ordered metric-like spaces, which generalize many results in corresponding literatures. An example is given to support our main results. As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.

Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Jamshaid Ahmad ◽  
Muhammad Arshad ◽  
Pasquale Vetro
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract.In this paper, we extend the coupled coincidence point theorems for a mixed

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