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On the linear equivalence of sequences in Hilbert spaces
Tariq Qawasmeh,Raed Hatamleh,Belal Batiha,Ahmed Heilat 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.2
A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.
FIXED AND COMMON FIXED POINT THEOREMS THROUGH MODIFIED ω−DISTANCE MAPPINGS
Qawasmeh Tariq,Tallafha Abdalla,Shatanawi Wasfi 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.2
In this paper, we introduce the notion of (k, φ, L)−mω contraction which based on the notion of ultra distance function. We employ our contraction to prove fixed and common fixed point theorems. Also, we introduce an example in order to support our work.
H-SIMULATION FUNCTIONS AND Ωb-DISTANCE MAPPINGS IN THE SETTING OF Gb-METRIC SPACES AND APPLICATION
Tariq Qawasmeh 경남대학교 수학교육과 2023 Nonlinear Functional Analysis and Applications Vol.28 No.2
The conceptions of generalized b-metric spaces or Gb-metric spaces and a gener- alized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ωb(H,θ,s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of H-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.
DISCUSSION ON b-METRIC SPACES AND RELATED RESULTS IN METRIC AND G-METRIC SPACES
Anwar Bataihah,Tariq Qawasmeh,Mutaz Shatnawi 경남대학교 수학교육과 2022 Nonlinear Functional Analysis and Applications Vol.27 No.2
In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (θ,φ)s-contraction of a map f in a b-metric space (M,db). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.
Ahmad AL-Zghoul,Tariq Qawasmeh,Raed Hatamleh,Abedalkareem Alhazimeh 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.4
In this manuscript, we formulate the notion of $\Omega(H,\theta)$-contraction on a self mapping $f:W\to W$, this contraction based on the concept of $\Omega$-distance mappings equipped on $G$-metric spaces together with the concept of $\cH $-simulation functions and the class of $\Theta$-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.