scholarly journals Some new results for Reich type mappings on cone b-metric spaces over Banach algebras

2018 ◽  
Vol 8 (2) ◽  
pp. 54-60 ◽  
Author(s):  
Jelena Vujaković ◽  
Abba Auwalu ◽  
Vesna Šešum-Čavić
Keyword(s):  
Metric Spaces ◽  
Banach Algebras

scholarly journals Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 135
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Nonlinear Operators ◽  
Complex Valued ◽  
Cone Metric

It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces.

scholarly journals Pentagonal Cone b-metric Spaces over Banach Algebras and Fixed Point Theorem of Generalized Lipschitz Mapping

2018 ◽  
Vol 22 ◽  
pp. 01003 ◽  
Author(s):  
Abba Auwalu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Lipschitz Mapping ◽  
Banach Fixed Point Theorem ◽  
Cone Metric ◽  
Generalized Lipschitz Mapping

In this paper, we introduce the concept of pentagonal cone b-metric space over Banach algebras as a generalization of cone metric space over Banach algebras and many of its generalizations. Furthermore, we prove Banach fixed point theorem in such a space. Our result unify, complement and/or generalized some recent results in the papers [1–7], and many others. We provide some examples to elucidate the validity and superiority of our results.

scholarly journals Fixed Point Results for Weakφ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Biwen Li ◽  
Huaping Huang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Uniqueness Of A Solution ◽  
Cone Metric

By using a nontrivial proof method, the purpose of this paper is to obtain some fixed point results for weakφ-contractions in cone metric spaces over Banach algebras. Several examples and applications to the existence and uniqueness of a solution to two classes of equations are also given.

scholarly journals Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Doaa Filali ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Banach Algebras ◽  
System Of Integral Equations ◽  
Different Types ◽  
Common Fixed Point Theorems

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

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